When to Use the Power of a Power Rule
Definition: (xa)b= xa * b
When this works: When raising a power to another power.
Use the Power of a Power Rule in These Situations:
- (x3)5
- (x2y15z12)4
1. Example: Power of a Power with Constants
Simplify (34)2
Keep the base and multiply the exponents: (34)2= 34 * 2 =38
Why does this work?
Rewrite (34)2
(34)2 = 34 * 34 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3
How many 3's are there? 8
2. Example: Power of a Power with a Variable
Simplify (x5)2
Power of a Power Rule: (xa)b= xa * b
In other words, keep the base and multiply the exponents.
(x5)2 = x5 * 2 = x10
Why does this work?
Rewrite (x5)2.
(x5)2= x5 * x5 = x * x * x * x * x * x * x * x * x * x
How many 5's are there? 10
3. Power of a Power Practice
Simplify the following:
1. (x-3)-5
2. (25)5
3. (10x)y
4. (-83)(x + 1)
5. (p4)¼
6. (ex)2