1. Simplify the following1) 2) 3) 4) 5) 6)

2. 12.03 Powers Raised to a Power

3. ( 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.

4. 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

5. 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

6. 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