Simplify the following

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Simplify the following 1) 2) 3) 4) 5) 6)

12.03 Powers Raised to a Power

( x 5 ) 3 = x 5 · x 5 · x 5 = x 15 ( 6x 4 ) 2 = 6x 4 · 6x 4 = 36x 8 Look at the following examples: ( x 5 ) 3 = x 5 · x 5 · x 5 = x 15 ( 6x 4 ) 2 = 6x 4 · 6x 4 = 36x 8 We want to find a rule to eliminate all these steps. When raising a power to another power, multiply the exponents. If there are coefficients, raise the coefficients to that power.

Simplify the following Rules: ( x 4 ) 7 = x 4 · 7 = x 28 ( a m ) n = a m · n ( y 3 ) – 2 = y 3(– 2) = y – 6 ( ab ) m = a m b m ( 9x 6 ) 2 = 9 2 · ( x 6 ) 2 = 81x 12 ( x 4y 5 ) 3 = ( x 4 ) 3 · ( y 5 ) 3 = x 12y 15 a m __ a m ( x 7 ) 8 x 56 __ 8 ____ ____ = = = b b m ( y 3 ) 8 y 24

Simplify the following ( x 6 ) 8 = x 48 ( y 2 ) – 9 = y – 18 ( 7x 3 ) 2 = 49x 6 ( 2x ) 5 = 32x 5 (– 2x 5y 6 ) 3 = – 8x 15y 18 (5x – 2 y 7 ) 2 = 25x – 4 y 14 27x 12 4 ____ x 24 3 _____ = = y 8 64y 15

Simplify the following Try This: Simplify the following ( x 9 ) 8 = x 72 ( y 4 ) – 9 = y – 36 ( 6x 5 ) 2 = 36x 10 ( 3x ) 4 = 81x 4 (– 2x 3y 4 ) 5 = – 32x 15y 20 x 42 6 ____ 7 x – 42 _____ = = y 18 y 63 4 16x 24 _____ = 81y 8