Write in Exponential Form ( fifth root of mn)^2

${(\sqrt[5]{m n})}^{2}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[5]{m n}$ as ${(m n)}^{\frac{1}{5}}$ .

${({(m n)}^{\frac{1}{5}})}^{2}$

Step 2

Multiply the exponents in ${({(m n)}^{\frac{1}{5}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(m n)}^{\frac{1}{5} \cdot 2}$

Combine $\frac{1}{5}$ and $2$ .

${(m n)}^{\frac{2}{5}}$