# What number raised to the 5th power equals 32?

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K_Marie Share
Nov 7, 2015

$x$ = 2

#### Explanation:

${x}^{5}$ = 32
$5 \sqrt{{x}^{5}}$ = $5 \sqrt{32}$
$x$ = 2

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May 2, 2016

$\sqrt[5]{32} = 2$

${2}^{5} = 32$

#### Explanation:

In questions dealing with indices, powers, roots of numbers, it is always useful to express a number as the product of its prime factors. If you know what a number is made up of, you know everything there is to know!

32 = 2x2x2x2x2 = ${2}^{5}$

It will be to your advantage to learn all the powers up to 1000.

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Nov 7, 2015

If you're totally forbidden from using a calculator, you can write it out algebraically and try out some integers that seem like they may work.

#### Explanation:

The question is: what number $x$ equals $32$ when it is taken to the fifth power, or symbolically,

${x}^{5} = 32$.

You can make it easier to check out some values in your head if you break up the left hand side:

$x {x}^{2} {x}^{2} = 32$.

Obviously $1$ isn't going to work, because the left hand side would be $1$. Don't even try $3$, because ${3}^{2} = 9$ and ${9}^{2} = 81$. However:

$\left(2\right) \left(4\right) \left(4\right) = \left(2\right) \left(16\right) = 32$.

Bingo! Of course if you can use a calculator, take the fifth root of both sides:

x=(32)^{\frac{1}{5}.

Cheers!

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