Write in Exponential Form ( fourth root of p^2)^8

${(\sqrt[4]{p^{2}})}^{8}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{p^{2}}$ as $p^{\frac{2}{4}}$ .

${(p^{\frac{2}{4}})}^{8}$

Step 2

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

${(p^{\frac{2 (1)}{4}})}^{8}$

Cancel the common factors.

Factor $2$ out of $4$ .

${(p^{\frac{2 \cdot 1}{2 \cdot 2}})}^{8}$

Cancel the common factor.

${(p^{\frac{2 \cdot 1}{2 \cdot 2}})}^{8}$

Rewrite the expression.

${(p^{\frac{1}{2}})}^{8}$

Step 3

Multiply the exponents in ${(p^{\frac{1}{2}})}^{8}$ .

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

$p^{\frac{1}{2} \cdot 8}$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$p^{\frac{1}{2} \cdot (2 (4))}$

Cancel the common factor.

$p^{\frac{1}{2} \cdot (2 \cdot 4)}$

Rewrite the expression.

$p^{4}$