Simplify ((4y^4)/(8y^0))^2

${(\frac{4 y^{4}}{8 y^{0}})}^{2}$

Move $y^{0}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(\frac{4 y^{4} y^{0}}{8})}^{2}$

Multiply $y^{4}$ by $y^{0}$ by adding the exponents.

Move $y^{0}$ .

${(\frac{4 (y^{0} y^{4})}{8})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{4 y^{0 + 4}}{8})}^{2}$

Add $0$ and $4$ .

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

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4 y^{4}$ .

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

Cancel the common factors.

Factor $4$ out of $8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

Apply the product rule to $\frac{y^{4}}{2}$ .

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

Multiply the exponents in ${(y^{4})}^{2}$ .

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

$\frac{y^{4 \cdot 2}}{2^{2}}$

Multiply $4$ by $2$ .

$\frac{y^{8}}{2^{2}}$

Raise $2$ to the power of $2$ .

$\frac{y^{8}}{4}$