do now exponent rules pre-assessment. agenda handouts package for part zero
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Do Now
• Exponent Rules pre-assessment
Agenda
• Handouts Package for part zero.
Exponent RulesOr Laws of Exponents
Base
x
Exponent
Remember!
4
In an expression of the form an, a is the base, n is the exponent, and the quantity an is called a power. The exponent indicates the number of times that the base is used as a factor.
24 is read “2 to the fourth power.” Reading Math
Zero Rules
Example:
Is undefined
One Rules
Example:
More Rules
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.
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.
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.
Simplify the expression.
Example 2A: Simplifying Expressions with Negative Exponents
The reciprocal of .
3–2
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
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
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.
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.
RAISING A POWER TO A POWER
Reading Math
(94)5 is read as “nine to the fourth power, to the fifth power.”
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.
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.
Work on PackageExponential Properties Practice
Exponential Properties
Picture Perfect