Write in Exponential Form ( seventh root of 5ab^2)^5

${(\sqrt[7]{5 a b^{2}})}^{5}$

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[7]{5 a b^{2}}$ as ${(5 a b^{2})}^{\frac{1}{7}}$ .

${({(5 a b^{2})}^{\frac{1}{7}})}^{5}$

Multiply the exponents in ${({(5 a b^{2})}^{\frac{1}{7}})}^{5}$ .

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

${(5 a b^{2})}^{\frac{1}{7} \cdot 5}$

Combine $\frac{1}{7}$ and $5$ .

${(5 a b^{2})}^{\frac{5}{7}}$