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## #3791. Multiplying and Dividing Powers

Mathematics, level: Middle
Posted Wed May 31 05:49:39 PDT 2006 by Judy (judyl_nguyen@yahoo.com).
Spring View Middle School, Huntington Beach, CA

6.6 Multiplying and Dividing Powers

I. Multiplying Powers
Do you think there is a shortcut rule?

x5  x4 = ( x  x  x  x  x )  ( x  x  x  x )

= x9

For #1 and 2, use repeated multiplication and then use the exponent rule to multiply the powers.

Ex. 1 35  3

a. (3  3  3  3  3 )  ( 3 )
= 36

b. 35 -- 1
= 36

Ex. 2 −2 2  −2 3
3 3

a. −2  −2  −2  −2  −2  −2
3 3 3 3 3 3

= −2 5
3

b. −2 2 + 3
3

= −2 5
3
NS 2.3,
AF 2.2

This rule only applies to powers w/ common bases.

When multiplying powers with the same bases,

Ex. 3 Simplify the expression 5a3  4a.

= (5  4)  (a3 − 1)

= 20a2

II. Dividing Powers
Can you predict the shortcut rule for dividing powers?

Ex. 4 Use repeated multiplication and then use the exponent rule to divide the powers.

(−10)4
(−10)2

a. = (−10)  (−10)  (−10)  (−10)
(−10)  (−10)

= (−10)2

b. = (−10)4−2

= (−10)2

Ex. 5 Simplify the expression.

−16x8y
−24x3

= − 2  ( x8−3 )  y
− 3

= 2x5y or 2 x5y
3 3
First,

When dividing powers w/ the same bases,

Ex. 6 In the United States, we use the 3-digit area code for phone numbers. Each digit can be any integer from 0 to 9. How many 3-digit area codes are possible? Express the answer as a power.

_______ _______ _______
Hundreds Tens Ones

10  10  10

= 103