# How do you write root5(32) as a fractional exponent?

${32}^{\frac{1}{5}} = {\left({2}^{5}\right)}^{\frac{1}{5}} = {2}^{5 \times \left(\frac{1}{5}\right)} = {2}^{\frac{5}{5}} = {2}^{1} = 2$

#### Explanation:

We can write

$\sqrt[5]{32}$

using a fractional exponent this way:

${32}^{\frac{1}{5}}$

But we can rewrite $32 = {2}^{5}$, and so:

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

We can use the rule that ${\left({x}^{a}\right)}^{b} = {x}^{a b}$ to say that:

${\left({2}^{5}\right)}^{\frac{1}{5}} = {2}^{5 \times \left(\frac{1}{5}\right)} = {2}^{\frac{5}{5}} = {2}^{1} = 2$

So we can write 2 with an exponential as ${2}^{1}$