Simplify ((xy^4)/(-4z^8))^2

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

Move the negative in front of the fraction.

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

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

Apply the product rule to $- \frac{x y^{4}}{4 z^{8}}$ .

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

Apply the product rule to $\frac{x y^{4}}{4 z^{8}}$ .

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

Apply the product rule to $x y^{4}$ .

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

Apply the product rule to $4 z^{8}$ .

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

Simplify the expression.

Raise $- 1$ to the power of $2$ .

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

Multiply $\frac{x^{2} {(y^{4})}^{2}}{4^{2} {(z^{8})}^{2}}$ by $1$ .

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

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

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

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

Multiply $4$ by $2$ .

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

Simplify the denominator.

Raise $4$ to the power of $2$ .

$\frac{x^{2} y^{8}}{16 {(z^{8})}^{2}}$

Multiply the exponents in ${(z^{8})}^{2}$ .

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

$\frac{x^{2} y^{8}}{16 z^{8 \cdot 2}}$

Multiply $8$ by $2$ .

$\frac{x^{2} y^{8}}{16 z^{16}}$