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Mathematics |

Posted Wed May 31 05:49:39 PDT 2006 by Judy (judyl_nguyen@yahoo.com).

Spring View Middle School, Huntington Beach, CA

Materials Required: Overhead projector, transparencies

6.6 Multiplying and Dividing PowersI. 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 )

= 36b. 35 -- 1

= 36Ex. 2 −2 2 −2 3

3 3a. −2 −2 −2 −2 −2 −2

3 3 3 3 3 3= −2 5

3b. −2 2 + 3

3= −2 5

3

NS 2.3,

AF 2.2This 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)

= 20a2II. 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)2a. = (−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 Ones10 10 10

= 103