Download - Exponents and Radicals Objective: To review rules and properties of exponents and radicals
![Page 1: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/1.jpg)
Exponents and Radicals
Objective: To review rules and properties of exponents and
radicals.
![Page 2: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/2.jpg)
Exponential Notation
![Page 3: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/3.jpg)
Properties of Exponents
![Page 4: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/4.jpg)
Properties of Exponents
![Page 5: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/5.jpg)
Example 1
• Use the properties of exponents to simplify each expression.
a) )4)(3( 34 abab
![Page 6: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/6.jpg)
Example 1
• Use the properties of exponents to simplify each expression.
a) )4)(3( 34 abab
baabab 234 12)4)(3(
![Page 7: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/7.jpg)
Example 1
• Use the properties of exponents to simplify each expression. You Try:
b) 32 )2( xy
![Page 8: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/8.jpg)
Example 1
• Use the properties of exponents to simplify each expression. You Try:
b) 32 )2( xy
63323332 8)(2)2( yxyxxy
![Page 9: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/9.jpg)
Example 1
• Use the properties of exponents to simplify each expression. You Try:
c) 02 )4(3 aa
![Page 10: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/10.jpg)
Example 1
• Use the properties of exponents to simplify each expression. You Try:
c) 02 )4(3 aa
0,3)1(3)4(3 02 aaaaa
![Page 11: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/11.jpg)
Example 1
• Use the properties of exponents to simplify each expression. You Try:
d) 235
y
x
![Page 12: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/12.jpg)
Example 1
• Use the properties of exponents to simplify each expression. You Try:
d) 235
y
x
2
6
2
23223 25)(55
y
x
y
x
y
x
![Page 13: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/13.jpg)
Example 2
• Rewrite each expression with positive exponents.
a) 1x
![Page 14: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/14.jpg)
Example 2
• Rewrite each expression with positive exponents.
a) 1x
xx
11
![Page 15: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/15.jpg)
Example 2
• Rewrite each expression with positive exponents.
b) 23
1x
![Page 16: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/16.jpg)
Example 2
• Rewrite each expression with positive exponents.
b) 23
1x
3
1
3
1
3
1 2
22
x
xx
![Page 17: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/17.jpg)
Example 2
• Rewrite each expression with positive exponents.• You Try:
c) ba
ba2
43
4
12
![Page 18: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/18.jpg)
Example 2
• Rewrite each expression with positive exponents.• You Try:
c) ba
ba2
43
4
12
5
5
4
23
2
43 3
4
12
4
12
b
a
bb
aa
ba
ba
![Page 19: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/19.jpg)
Example 2
• Rewrite each expression with positive exponents.• You Try:
d) 223
y
x
![Page 20: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/20.jpg)
Example 2
• Rewrite each expression with positive exponents.• You Try:
d) 223
y
x
4
2
222
22
2
22
9)(33
3
x
y
x
y
x
y
y
x
![Page 21: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/21.jpg)
Radicals and Their Properties
• Definition of nth Root of a Number.• Let a and b be real numbers and let n > 2 be a
positive integer. If
a = bn
then b is an nth root of a. If n = 2, the root is a square root. If n = 3, the root is a cube root.
![Page 22: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/22.jpg)
Radicals and Their Properties
• Principal nth Root of a Number.• Let a be a real number that has at least one nth root.
The principal nth root of a is the nth root that has the same sign as a. It is denoted by a radical symbol
• The positive integer n is the index of the radical, and the number a is the radicand. If n = 2, omit the index and write .a
n a
![Page 23: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/23.jpg)
Example 5
• Evaluate:
a) 36
![Page 24: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/24.jpg)
Example 5
• Evaluate:
a)
636
36
![Page 25: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/25.jpg)
Example 5
• Evaluate:
b) 36
![Page 26: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/26.jpg)
Example 5
• Evaluate:
b)
636
36
![Page 27: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/27.jpg)
Example 5
• Evaluate:
c) 36
![Page 28: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/28.jpg)
Example 5
• Evaluate:
c)
DNE 36
36
![Page 29: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/29.jpg)
Example 5
• Evaluate:
d) 3
64
125
![Page 30: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/30.jpg)
Example 5
• Evaluate:
d) 3
64
125
4
5
64
125
64
1253
3
3
![Page 31: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/31.jpg)
Example 5
• Evaluate:• You Try:
d) 3
8
27
![Page 32: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/32.jpg)
Example 5
• Evaluate:• You Try:
d) 3
8
27
2
3
8
27
8
273
3
3
![Page 33: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/33.jpg)
Example 5
• Evaluate:
e) 5 32
![Page 34: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/34.jpg)
Example 5
• Evaluate:
e) 5 32
2325
![Page 35: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/35.jpg)
Properties of Radicals
![Page 36: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/36.jpg)
Properties of Radicals
![Page 37: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/37.jpg)
Example 6
• Use the properties of radical to simplify each expression.
a) 28
![Page 38: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/38.jpg)
Example 6
• Use the properties of radical to simplify each expression.
a) 28
41628
![Page 39: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/39.jpg)
Example 6
• Use the properties of radical to simplify each expression.
b) 33 5
![Page 40: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/40.jpg)
Example 6
• Use the properties of radical to simplify each expression.
b) 33 5
5555 133/133
![Page 41: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/41.jpg)
Example 6
• Use the properties of radical to simplify each expression.
c) 3 3x
![Page 42: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/42.jpg)
Example 6
• Use the properties of radical to simplify each expression.
c) 3 3x
xx 3/13
![Page 43: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/43.jpg)
Example 6
• Use the properties of radical to simplify each expression.
d) 6 6y
||6 6 yy
![Page 44: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/44.jpg)
Simplifying Radicals
• An expression involving radicals is in simplest form when the following conditions are satisfied.
1. All possible factors have been removed from the radical.
2. All fractions have radical-free denominators (accomplished by a process called rationalizing the denominator).
3. The index of the radical is reduced.
![Page 45: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/45.jpg)
Example 7
• Simplify each radical.
a) 32
![Page 46: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/46.jpg)
Example 7
• Simplify each radical.
a) 32
2421632
![Page 47: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/47.jpg)
Example 7
• Simplify each radical.• You Try:
a) 24
![Page 48: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/48.jpg)
Example 7
• Simplify each radical.• You Try:
a) 24
626424
![Page 49: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/49.jpg)
Example 7
• Simplify each radical.
b) 4 48
![Page 50: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/50.jpg)
Example 7
• Simplify each radical.
b) 4 48
4444 3231648
![Page 51: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/51.jpg)
Example 7
• Simplify each radical.
c) 375x
![Page 52: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/52.jpg)
Example 7
• Simplify each radical.
c) 375x
xxxxx 3532575 23
![Page 53: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/53.jpg)
Example 7
• Simplify each radical.• You Try:
c) 548x
![Page 54: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/54.jpg)
Example 7
• Simplify each radical.• You Try:
c) 548x
xxxxx 3431648 245
![Page 55: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/55.jpg)
Example 8
• Simplify each radical.
a) 3 24
![Page 56: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/56.jpg)
Example 8
• Simplify each radical.
a) 3 24
3333 323824
![Page 57: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/57.jpg)
Example 8
• Simplify each radical.
b) 3 424a
![Page 58: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/58.jpg)
Example 8
• Simplify each radical.
b) 3 424a
333 3333 4 323824 aaaaa
![Page 59: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/59.jpg)
Example 8
• Simplify each radical.• You Try:
c) 3 640x
![Page 60: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/60.jpg)
Example 8
• Simplify each radical.• You Try:
c) 3 640x
323 6333 6 525840 xxx
![Page 61: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/61.jpg)
Example 9
• Combine each radical.
a) 273482
![Page 62: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/62.jpg)
Example 9
• Combine each radical.
a) 273482
3933162273482
33938
![Page 63: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/63.jpg)
Example 9
• Combine each radical.• You Try:
b) 3 43 5416 xx
![Page 64: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/64.jpg)
Example 9
• Combine each radical.• You Try:
b) 3 43 5416 xx
33 3333 43 227285416 xxxxx
333 2)32(2322 xxxxx
![Page 65: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/65.jpg)
Example 10
• Rationalize the denominator of each expression.
a) 3
5
![Page 66: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/66.jpg)
Example 10
• Rationalize the denominator of each expression.
a) 3
5
3
35
3
3
3
5
![Page 67: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/67.jpg)
You Try
• Rationalize the denominator of each expression.• You Try:
b) 2
1
![Page 68: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/68.jpg)
Example 10
• Rationalize the denominator of each expression.• You Try:
b) 2
1
2
2
2
2
2
1
![Page 69: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/69.jpg)
Example 11
• Rationalize the denominator of each expression.
a) 73
2
7379
)73(2
)73(
)73(
)73(
2
![Page 70: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/70.jpg)
You Try
• Rationalize the denominator of each expression.• You Try:
b) 54
3
![Page 71: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/71.jpg)
You Try
• Rationalize the denominator of each expression.• You Try:
b) 54
3
11
5312
)54(
)54(
)54(
3
![Page 72: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/72.jpg)
Rational Exponents
• The numerator of a rational exponent denotes the power to which the base is raised, and the denominator denotes the index or the root to be taken.
![Page 73: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/73.jpg)
Example 13
• Change the base from radical to exponential form.
a) 3
![Page 74: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/74.jpg)
Example 13
• Change the base from radical to exponential form.
a) 3
2/133
![Page 75: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/75.jpg)
Example 13
• Change the base from radical to exponential form.
b) 5x
![Page 76: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/76.jpg)
Example 13
• Change the base from radical to exponential form.
b) 5x
2/52/155 )( xxx
![Page 77: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/77.jpg)
You Try
• Change the base from radical to exponential form.• You Try:
c) 3 4y
![Page 78: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/78.jpg)
You Try
• Change the base from radical to exponential form.• You Try:
c) 3 4y
3/43/143 4 )( yyy
![Page 79: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/79.jpg)
Example 14
• Change the base from exponential to radical form.
a) 2/3)( yx
![Page 80: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/80.jpg)
Example 14
• Change the base from exponential to radical form.
a) 2/3)( yx
32/3 )()( yxyx
![Page 81: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/81.jpg)
You Try
• Change the base from exponential to radical form.
b) 4/14/3 yx
![Page 82: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/82.jpg)
You Try
• Change the base from exponential to radical form.
b) 4/14/3 yx
4 34/134/14/3 )( yxyxyx
![Page 83: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/83.jpg)
Example 15
• Simplify each rational expression.
a) 5/3)32(
![Page 84: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/84.jpg)
Example 15
• Simplify each rational expression.
a) 5/3)32(
8)2())32(()32( 335/15/3
![Page 85: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/85.jpg)
Example 15
• Simplify each rational expression.• You Try:
b) 3/2)27(
![Page 86: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/86.jpg)
Example 15
• Simplify each rational expression.• You Try:
b) 3/2)27(
9
1)3())27(()27( 223/13/2
![Page 87: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/87.jpg)
You Try
• Simplify each rational expression.• You Try:
c) 3/2)64(
![Page 88: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/88.jpg)
You Try
• Simplify each rational expression.• You Try:
c) 3/2)64(
164))64(()64( 223/13/2
![Page 89: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/89.jpg)
You Try
• Simplify each rational expression.• You Try:
d) 4/3)16(
![Page 90: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/90.jpg)
You Try
• Simplify each rational expression.• You Try:
d) 4/3)16(
8
12))16(()16( 334/14/3
![Page 91: Exponents and Radicals Objective: To review rules and properties of exponents and radicals](https://reader036.vdocuments.net/reader036/viewer/2022081501/5697bf941a28abf838c90372/html5/thumbnails/91.jpg)
Homework
• Pages 21-22
• 5-11 odd
• 17-35 odd
• 51-72 multiples of 3