Evaluate (4 fourth root of y^5)^(1/2)

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

Factor out $y^{4}$ .

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

Pull terms out from under the radical.

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $4 y \sqrt[4]{y}$ .

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

Apply the product rule to $4 y$ .

$4^{\frac{1}{2}} y^{\frac{1}{2}} {\sqrt[4]{y}}^{\frac{1}{2}}$

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$2^{1} y^{\frac{1}{2}} {\sqrt[4]{y}}^{\frac{1}{2}}$

Evaluate the exponent.

$2 y^{\frac{1}{2}} {\sqrt[4]{y}}^{\frac{1}{2}}$