exponents and scientific notation 5.1 1.evaluate exponential forms with integer exponents. 2.write...
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Exponents and Scientific Notation5.15.1
1. Evaluate exponential forms with integer exponents.2. Write scientific notation in standard form.3. Write standard form numbers in scientific notation.
Objective 1
Evaluate exponential forms with integer exponents.
When an equation in one variable is solved the answer is a point on a line.
Identify the base, exponent and evaluate.Identify the base, exponent and evaluate.
Base:
Exponent:
Value:
52
42
32
42
Base:
Exponent:
Value:
Base:
Exponent:
Value:
Base:
Exponent:
Value:
2
5
32
-2
3
-8
-2
4
16
2
4
-16
Evaluate: – 32
a) 9
b) –6
c) 6
d) 9
Evaluate: – 32
a) 9
b) –6
c) 6
d) 9
Evaluate:
a) -93
43253 2
b) 15
c) 105
d) None of the above
Evaluate:
a) -93
43253 2
b) 15
c) 105
d) None of the above
Evaluating Exponential Forms with Negative Bases
(negative number)even exponent = positive
(negative number)odd exponent = negative
When an equation in one variable is solved the answer is a point on a line.
Evaluate.Evaluate.
3
52
2
53
125
8
259
Raising a Quotient to a Power
If a and b are real numbers, where b 0 and n is a natural number, then
.
n n
n
a a
b b
0
1
2
3
4
3
33
93
273
813Observe the pattern….
1
Zero as an Exponent
If a is a real number and then 0,a 0 1.a
When an equation in one variable is solved the answer is a point on a line.
Evaluate:Evaluate:
05
05
05
0
251
1 1
– 1 1
When an equation in one variable is solved the answer is a point on a line.
Evaluate:Evaluate:
06y
07
06y
00 43
61
– 1
1 – 1 = 0
When an equation in one variable is solved the answer is a point on a line.
Evaluate:Evaluate:
020 268 yxw
033 Indeterminate
-6x2
13
33
93
273
813
0
1
2
3
4
Observe the pattern….
33
22
11
3
1271
3
3
191
3
3
131
3
Negative exponents are POSITIONAL only!!!Negative exponents are POSITIONAL only!!!
If a is a real number, where a 0 and n is a natural
number, then 1
. nn
aa
Exponents must be positive before you can evaluate!!!
When an equation in one variable is solved the answer is a point on a line.
Simplify:Simplify:
32
34 x
23 x
35x
81
2
13 2
3
x
34
x
35x
35x
35 x 31
5x
1
53x
35x
Negative exponents are POSITIONAL only!!!Negative exponents are POSITIONAL only!!!
If a is a real number, where a 0 and n is a natural number, then
1. n
na
a
When an equation in one variable is solved the answer is a point on a line.
Simplify:Simplify:
2
32
b
a
3233 yx
3
42
c
ba
km
h2
54
232
ba
2
34
a
cb
3
233
y
x
kh
m5
24
23
x 23
1
x
231
x 2
91
x
91
2x
9
2x
2
3
x
If a and b are real numbers, where a 0 and b 0
and n is a natural number, then
.
n na b
b a
Slide 5- 24Copyright © 2011 Pearson Education, Inc.
Evaluate: – 2–6
a)
b)
c)
d) 64
12
1
64
1
64
5.1
Slide 5- 25Copyright © 2011 Pearson Education, Inc.
Evaluate: – 2–6
a)
b)
c)
d) 64
12
1
64
1
64
5.1
Objective 2
Write scientific notation in standard form.
Scientific notation: A number expressed in the form where a is a decimal number with and n is an integer.
10 ,na1 10 a
3
5
10452
10453
.
.
Write 875,000 in scientific notation.
758. 510
Write 0.0000000472 in scientific notation.
724. 810
54.26 10
Write in standard form:
= 426,000
Write in standard form:
43.87 10 = .000387
Slide 5- 32Copyright © 2011 Pearson Education, Inc.
Write 13,030,000 in scientific notation.
a)
b)
c)
d)
41303 10
613.03 10
71.303 10
90.1303 10
5.1
Slide 5- 33Copyright © 2011 Pearson Education, Inc.
Write 13,030,000 in scientific notation.
a)
b)
c)
d)
41303 10
613.03 10
71.303 10
90.1303 10
5.1
Slide 5- 34Copyright © 2011 Pearson Education, Inc.
Write in standard notation.
a) 4,690,000
b) 4,690,000,000
c) 0.000000469
d) 0.00000469
64.69 10
5.1
Write in standard notation.
a) 4,690,000
b) 4,690,000,000
c) 0.000000469
d) 0.00000469
64.69 10
5.1