Power of a Power

How to solve the power of a power (am)n: formula, 2 examples, and their solutions.

Formula

Formula

(am)n = am⋅n
The power of a power can be simplified by multiplying the exponents: m⋅n.

Example 1

Example

Solution

A power (x2) is powered (cubed).
So (x2)3 = x2⋅3.

2⋅3 = 6.

So x6 is the answer.

Example 2

Example

Solution

Simplify the inner part: (x4)2.
A power (x4) is powered (squared).
So (x4)2 = x4⋅2.

Think 4⋅2 as an exponent number.
A power [x4⋅2] is powered (fifth).
So [x4⋅2]5 = x4⋅2⋅5.

So ((x4)2)5 = x4⋅2⋅5.

Simplify the exponent.
4⋅2⋅5 = 8⋅5 = 40.

So x40 is the answer.