Simplify ((4x^3y^2)/(9xy^4))^2

${(\frac{4 x^{3} y^{2}}{9 x y^{4}})}^{2}$

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $4 x^{3} y^{2}$ .

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

Cancel the common factors.

Factor $x$ out of $9 x y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $y^{2}$ and $y^{4}$ .

Factor $y^{2}$ out of $4 x^{2} y^{2}$ .

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

Cancel the common factors.

Factor $y^{2}$ out of $9 y^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Apply the product rule to $\frac{4 x^{2}}{9 y^{2}}$ .

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

Apply the product rule to $4 x^{2}$ .

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

Apply the product rule to $9 y^{2}$ .

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

Simplify the numerator.

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

$\frac{16 {(x^{2})}^{2}}{9^{2} {(y^{2})}^{2}}$

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

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

$\frac{16 x^{2 \cdot 2}}{9^{2} {(y^{2})}^{2}}$

Multiply $2$ by $2$ .

$\frac{16 x^{4}}{9^{2} {(y^{2})}^{2}}$

Simplify the denominator.

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

$\frac{16 x^{4}}{81 {(y^{2})}^{2}}$

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

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

$\frac{16 x^{4}}{81 y^{2 \cdot 2}}$

Multiply $2$ by $2$ .

$\frac{16 x^{4}}{81 y^{4}}$