Write in Exponential Form ( fourth root of 5^3)^(1/2)

${(\sqrt[4]{5^{3}})}^{\frac{1}{2}}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{5^{3}}$ as $5^{\frac{3}{4}}$ .

${(5^{\frac{3}{4}})}^{\frac{1}{2}}$

Step 2

Multiply the exponents in ${(5^{\frac{3}{4}})}^{\frac{1}{2}}$ .

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

$5^{\frac{3}{4} \cdot \frac{1}{2}}$

Multiply $\frac{3}{4} \cdot \frac{1}{2}$ .

Multiply $\frac{3}{4}$ by $\frac{1}{2}$ .

$5^{\frac{3}{4 \cdot 2}}$

Multiply $4$ by $2$ .

$5^{\frac{3}{8}}$