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# Power of a product Calculator

## Get detailed solutions to your math problems with our Power of a product step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here.

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###  Difficult Problems

1

Here, we show you a step-by-step solved example of power of a product. This solution was automatically generated by our smart calculator:

$\left(2x^2\right)^{-4}$
2

Applying the property of exponents, $\displaystyle a^{-n}=\frac{1}{a^n}$, where $n$ is a number

$\frac{1}{\left(2x^2\right)^{4}}$
3

The power of a product is equal to the product of it's factors raised to the same power

$\frac{1}{2^{4}\left(x^2\right)^{4}}$
4

Calculate the power $2^{4}$

$\frac{1}{16\left(x^2\right)^{4}}$
5

Simplify $\left(x^2\right)^{4}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. In the expression, $m$ equals $2$ and $n$ equals $4$

$16x^{2\cdot 4}$
6

Multiply $2$ times $4$

$16x^{8}$
7

Multiply $2$ times $4$

$\frac{1}{16x^{8}}$

##  Final answer to the problem

$\frac{1}{16x^{8}}$

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