Page 264 - Algebra 1

L E S S O N Simplifying and Evaluating Expressions
40
Using the Power Property of Exponents
Warm Up
1. Vocabulary The is the number that tells how many times the
(3)
base of a power is used as a factor.
Simplify.
2. (4x2y3)(5x4y4)
_ 3 6 3. 24x y
(32) 36x5y3
5. Compare: 42 + √ 36 -(-3)2 + √ 25. Use >, <, or =.
(13)
(3)
4. (-3)2 - 32 (11)
New Concepts Previous lessons have explored expressions involving exponents. Several rules and definitions have been developed.
x0=1
x 1 = x
_m
x =xm-n
xn
xm·xn =xm+n x - n = _1
xn
There is another property of exponents that involves raising a power to a power.
Exploration Raising a Power to a Power
This Exploration shows how to raise a power to a power. The expression (24)3 means to use 24 as a factor three times.
Hint
Write in a 1 if there is no exponent for variables or numbers. For example, 4=41 andx=x1.
(24)3 =24 ·24 ·24 =212
a. (32)3 b. (45)2 c. (72)4
d. Are there any patterns? What conclusions can you draw from the patterns?
The expression (a2)3 means to use a2 as a factor three times. (a2)3 =a2 ·a2 ·a2 =a6
Simplify.
e. (a3)5 f. (b6)2
g. (d4)4
h. Using the results from a through g above, write a rule for raising a power to a power.
Simplify.
Math Reasoning
Generalize Use the meaning of powers and exponents to explain why (a2)3 = a6.
Online Connection www.SaxonMathResources.com
Lesson 40 249