Simplify (8/9xy^4)^2

${(\frac{8}{9} x y^{4})}^{2}$

Multiply $\frac{8}{9} (x y^{4})$ .

Combine $x$ and $\frac{8}{9}$ .

${(\frac{x \cdot 8}{9} y^{4})}^{2}$

Combine $\frac{x \cdot 8}{9}$ and $y^{4}$ .

${(\frac{x \cdot 8 y^{4}}{9})}^{2}$

Move $8$ to the left of $x$ .

${(\frac{8 \cdot x y^{4}}{9})}^{2}$

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

Apply the product rule to $\frac{8 x y^{4}}{9}$ .

$\frac{{(8 x y^{4})}^{2}}{9^{2}}$

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

$\frac{{(8 x)}^{2} {(y^{4})}^{2}}{9^{2}}$

Apply the product rule to $8 x$ .

$\frac{8^{2} x^{2} {(y^{4})}^{2}}{9^{2}}$

Simplify the numerator.

Raise $8$ to the power of $2$ .

$\frac{64 x^{2} {(y^{4})}^{2}}{9^{2}}$

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

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

$\frac{64 x^{2} y^{4 \cdot 2}}{9^{2}}$

Multiply $4$ by $2$ .

$\frac{64 x^{2} y^{8}}{9^{2}}$

Raise $9$ to the power of $2$ .

$\frac{64 x^{2} y^{8}}{81}$