Page 265 - Algebra 1

The pattern in the Exploration leads to the Power of a Power Property.
Power of a Power Property
If mandnarerealnumbersandx≠0,then (xm)n = xmn.
Example
1
Simplifying a Power of a Power
Simplify each expression. a. (23)2
SOLUTION
(23)2 = 23·2
= 26
b. (a6)3 SOLUTION
(a6)3 = a6·3
= a18
The Power of a Power Property and the Product Property of Exponents can be used together to formulate a rule for the power of a product. Look at the expression (5x2)3. The outer exponent of 3 means to use everything inside the parentheses as a factor three times, or to multiply 5x2 three times.
(5x2)3 = 5x2 · 5x2 · 5x2
=(5·5·5)·(x2 ·x2 ·x2)=53 ·x6 =125x6
This pattern is summarized in the Power of a Product Property.
Power of a Product Property
If misarealnumberwithx≠0andy≠0,then (xy)m = xmym.
Example
2
Simplifying a Power of a Product
Simplify each expression.
a. (7a3b5)3 SOLUTION
(7a3b5)3
=73 ·a3·3 ·b5·3
= 343a9b15
b. (-2y4)3 SOLUTION
(-2y4)3 =(-2)3 ·y4·3 = -8y12
Application: Interior Design
Math Reasoning
Write Explain the difference between the expression xm · xn and (xm)n.
Example
3
A square family room is being measured for carpeting. If the length of one side of the room is 2x feet, what is the area of the room?
SOLUTION
The area is (2x)2 = 4x2 square feet.
2x ft
250 Saxon Algebra 1
2x ft
2x ft
2x ft