Simplify ((3xy^4)/(5z^2))^2

${(\frac{3 x y^{4}}{5 z^{2}})}^{2}$

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

Apply the product rule to $\frac{3 x y^{4}}{5 z^{2}}$ .

$\frac{{(3 x y^{4})}^{2}}{{(5 z^{2})}^{2}}$

Apply the product rule to $3 x y^{4}$ .

$\frac{{(3 x)}^{2} {(y^{4})}^{2}}{{(5 z^{2})}^{2}}$

Apply the product rule to $3 x$ .

$\frac{3^{2} x^{2} {(y^{4})}^{2}}{{(5 z^{2})}^{2}}$

Apply the product rule to $5 z^{2}$ .

$\frac{3^{2} x^{2} {(y^{4})}^{2}}{5^{2} {(z^{2})}^{2}}$

Simplify the numerator.

Raise $3$ to the power of $2$ .

$\frac{9 x^{2} {(y^{4})}^{2}}{5^{2} {(z^{2})}^{2}}$

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

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

$\frac{9 x^{2} y^{4 \cdot 2}}{5^{2} {(z^{2})}^{2}}$

Multiply $4$ by $2$ .

$\frac{9 x^{2} y^{8}}{5^{2} {(z^{2})}^{2}}$

Simplify the denominator.

Raise $5$ to the power of $2$ .

$\frac{9 x^{2} y^{8}}{25 {(z^{2})}^{2}}$

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

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

$\frac{9 x^{2} y^{8}}{25 z^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{9 x^{2} y^{8}}{25 z^{4}}$