Write in Exponential Form ( fourth root of 10v)^5

${(\sqrt[4]{10 v})}^{5}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{10 v}$ as ${(10 v)}^{\frac{1}{4}}$ .

${({(10 v)}^{\frac{1}{4}})}^{5}$

Step 2

Multiply the exponents in ${({(10 v)}^{\frac{1}{4}})}^{5}$ .

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

${(10 v)}^{\frac{1}{4} \cdot 5}$

Combine $\frac{1}{4}$ and $5$ .

${(10 v)}^{\frac{5}{4}}$