properties of rational exponents
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Properties of Rational Exponents
Section 7.2
Agenda 1.Math Talk Expectations 2.Come up with what
happens when students do not follow expectations
3.Number Talk 4.Review Last weeks test 5.5. Start rational exponents!
Number Talk Devonte received $ 500 which was 115% of a number. He has to give 75% of that number to Larry. How much will Larry receive?
WHAT YOU WILL LEARN:1. Simplify expressions with rational exponents.2. Use properties of rational exponents.3. Write an expression involving rational exponents in simplest form.4. Perform operations with rational exponents.5. Simplify expressions that have variables and rational exponents.6. Write an expression involving variables and rational exponents in simplest form.7. Perform operations with rational exponents and variables.
Properties of Rational Exponents
nmnm aaa
Properties of Rational Exponents:
Property: Example:
1.
2. (am)n = amn
3. (ab)m = ambm
4.
93333 2)23
21(
23
21
6444)4( 3)223(22
3
62349)49( 21
21
21
0,1 aa
a mm
51
25
12521
21
Properties of Rational Exponents (cont.)
0, aaaa nmn
m
Properties of Rational Exponents:
Property: Example:
5.
6.
36666
6 2)21
25(
21
25
0,)( aba
ba
m
mm
32
27
8)278(
31
31
31
Using the Properties
41
21
55
• Simplify the expressions:1.
2.
3.
231
21
)58(
41
44 )32(
More Fun with Properties
31
7
74.
5. 2
31
31
)4
12(
You Try
3
41
41
32
31
33
241
31
31
21
9
18
6
6)24(
)627(
66
• Simplify:1.2.3.4.
5.
More Simplifying
33 164
• Simplify the expressions:1.
2. 4
4
2162
You Try
33 525
• Simplify:1.
2. 3
3
432
Simplest Form - continued
3 54
• In order for a radical to be in simplest form, you have to remove any perfect nth powers and rationalize denominators. Example:
Write in simplest form:1. 2. 5
43
You Try
4
4
87
64
• Write in simplest form:1.
2.
Operations Using Radicals
)6(2)6(7 51
51
• Two radicals expressions are “like radicals” if they have the same index and the same radicand. Example:
• Perform the indicated operation:1. 2. 33 216
You Try
33
43
43
381
)4(3)4(5
• Perform the indicated operation:
1.
2.
Simplifying Expressions Involving Variables
nn x
• Important!
= x when n is odd.
= |x| when n is even.
nn x
Simplifying
3 6125y
• Simplify the expression. Assume all variables are positive:
1. 2.
3. 4.
21
102 )9( vu
48
4
yx
531
21
2
6
zx
xy
You Try
341
32
410
5
21
24
3 9
6
18
)16(
27
tr
rs
yx
hg
z
• Simplify the expression. Assume all variables are positive.
1.2.3.
4.
Writing Variable Expressions in Simplest Form
5 13955 cba
• Write the expression in simplest form. Assume all variables are positive.
1. 2. 37yx
You Try
57
2
4 149412
hg
fed
• Write the expression in simplest form. Assume all variables are positive.
1.
2.
Adding and Subtracting Expressions Involving Variables
yy 65
• Perform the indicated operation. Assume all variables are positive.
1. 2.
3.
31
31
72 xyxy
3 23 5 4053 xxx
You Try
44 5
41
41
662
63
38
xxx
ghgh
xx
• Perform the indicated operations. Assume all variables are positive.
1.
2.
3.
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