Write in Exponential Form ( square root of 6v)^3

${(\sqrt{6 v})}^{3}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{6 v}$ as ${(6 v)}^{\frac{1}{2}}$ .

${({(6 v)}^{\frac{1}{2}})}^{3}$

Step 2

Multiply the exponents in ${({(6 v)}^{\frac{1}{2}})}^{3}$ .

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

${(6 v)}^{\frac{1}{2} \cdot 3}$

Combine $\frac{1}{2}$ and $3$ .

${(6 v)}^{\frac{3}{2}}$