# Power of a Power

How to solve the power of a power (a^{m})^{n}: formula, 2 examples, and their solutions.

## Formula

(a^{m})^{n} = a^{m⋅n}

The power of a power can be simplified by

multiplying the exponents: m⋅n.

## Example(x^{2})^{3}

Solution

Solution (Detail)

(x^{2})^{3} = x^{2⋅3}

2⋅3 = 6.

So x^{6} is the answer.

## Example[(x^{4})^{2}]^{5}

Solution

Solution (Detail)

Start from the inner part.

(x^{4})^{2} = x^{4⋅2}

4⋅2 = 8

[x^{8}]^{5} = x^{8⋅5}

8⋅5 = 40

So x^{40} is the answer.