# Power of a Power

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

## Formula

### Formula

(a^{m})^{n} = a^{m⋅n}

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

## Example 1

### Example

### Solution

A power (x^{2}) is powered (cubed).

So (x^{2})^{3} = x^{2⋅3}.

2⋅3 = 6.

So x^{6} is the answer.

## Example 2

### Example

### Solution

Simplify the inner part: (x^{4})^{2}.

A power (x^{4}) is powered (squared).

So (x^{4})^{2} = x^{4⋅2}.

Think 4⋅2 as an exponent number.

A power [x^{4⋅2}] is powered (fifth).

So [x^{4⋅2}]^{5} = x^{4⋅2⋅5}.

So ((x^{4})^{2})^{5} = x^{4⋅2⋅5}.

Simplify the exponent.

4⋅2⋅5 = 8⋅5 = 40.

So x^{40} is the answer.