Simplify ( square root of y^(1/4))^8

${(\sqrt{y^{\frac{1}{4}}})}^{8}$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{y^{\frac{1}{4}}}$ as $y^{\frac{\frac{1}{4}}{2}}$ .

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

Step 2

Multiply the numerator by the reciprocal of the denominator.

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

Step 3

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

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

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

Multiply $4$ by $2$ .

${(y^{\frac{1}{8}})}^{8}$

Step 4

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

$y^{\frac{1}{8} \cdot 8}$

Step 5

Combine $\frac{1}{8}$ and $8$ .

$y^{\frac{8}{8}}$

Step 6

Cancel the common factor of $8$ .

Cancel the common factor.

$y^{\frac{8}{8}}$

Rewrite the expression.

$y^{1}$

Step 7

Simplify.

$y$