Evaluating Algebraic Expressions 4-3 Properties of Exponents Warm Up California Standards California Standards Lesson Presentation Preview Preview
Evaluating Algebraic Expressions 4-3 Properties of Exponents Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview.
Dec 23, 2015
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Evaluating Algebraic Expressions
4-3 Properties of Exponents
Warm Up
California StandardsCalifornia Standards
Lesson Presentation
PreviewPreview
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Warm UpEvaluate.
271. 33
2. 4 • 4 • 4 • 4
3. b2 for b = 4
4. n2r for n = 3 and r = 2
256
16
18
Evaluating Algebraic Expressions
4-3 Properties of Exponents
California Standards
NS2.3 Understand negative whole-number exponents. Multiply and divide expressions involving exponents with a common base. NS2.1 Multiply, divide, and simplify rational numbers by using exponent rules.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
The following suggests a rule for multiplying powers with the same base.
24 • 22 = (2 • 2 • 2 • 2) • (2 • 2) = 26
a3 • a2 = (a • a • a) • (a • a) = a5
Notice that the sum of the exponents in each expression equals the exponent in the answer: 4 + 2 = 6 and 3 + 2 = 5.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Additional Example 1: Multiplying Powers with the Same Base
A. 66 • 63
69
66 + 3
B. n5 • n7
n12
n5 + 7
Add exponents.
Add exponents.
Simplify each expression. Write your answer in exponential form.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Check It Out! Example 1
A. 42 • 44
46
42 + 4
B. x2 • x3
x5
x2 + 3
Add exponents.
Add exponents.
Simplify each expression. Write your answer in exponential form.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
The following suggests a rule for dividing powers with the same base.
Notice that the difference between the exponents in each expression equals the exponent in the answer: 6 – 2 = 4 and 5 – 3 = 2.
36
32= = 3 • 3 • 3 • 3 = 34
3 33 3 3 3 3 31 1
1 1
x5
x3= = x • x = x2
x x xx x x x x1 1 1
1 1 1
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Subtract exponents.
72
75 – 3
75
73
Additional Example 2: Dividing Powers with the Same Base
Simplify each expression. Write your answer in exponential form.
A.
x10
x9B.
Subtract exponents.x10 – 9
x Think: x = x1
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Subtract exponents.
97
99 – 2
99
92
Check It Out! Example 2
A.
B. e10
e5
Subtract exponents.e10 – 5
e5
Simplify each expression. Write your answer in exponential form.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
RAISING A POWER TO A POWER
To see what happens when you raise a power to a power, use the order of operations.
(c3)2 = (c ● c ● c)2
= (c ● c ● c) ● (c ● c ● c)
= c6
Show the power inside the parentheses.
Show the power outside the parentheses.
Simplify.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
RAISING A POWER TO A POWER
Reading Math
(94)5 is read as “nine to the fourth power, to the fifth power.”
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Simplify each expression. Write your answer in exponential form.
Multiply exponents.
Additional Example 3: Raising a Power to a Power
A. (54)2
(54)2
54 • 2
58 B. (67)9
(67)9
67 • 9
663
Multiply exponents.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Multiply exponents.
Additional Example 3: Raising a Power to a Power
C. D. (172)–20
172 • –20
17–40
2 3
12 • –3
Simplify each expression. Write your answer in exponential form.
2 3
–36
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Multiply exponents.
Check It Out! Example 3
A. (33)4
(33)4
33 • 4
312 B. (48)2
(48)2
48 • 2
416
Multiply exponents.
Simplify each expression. Write your answer in exponential form.
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Multiply exponents.
Check It Out! Example 3
C. D. (134)–10
134 • –10
13–40
1 4
11• –2
Simplify each expression. Write your answer in exponential form.
1 4
–22
Evaluating Algebraic Expressions
4-3 Properties of Exponents
Lesson Quiz
3.
8 9n 71. n3 n4
109
105 10 4 4.
t 2
5. 32 • 33 • 35 3 10
2. 8 • 88
t9
t7
6. (m2)19 m38
7. (9-8)9 8. (104)0 1
Simplify each expression. Write your answer in exponential form.
1972
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