Simplify ((4x^7)/(x^2y^4))^2

${(\frac{4 x^{7}}{x^{2} y^{4}})}^{2}$

Cancel the common factor of $x^{7}$ and $x^{2}$ .

Factor $x^{2}$ out of $4 x^{7}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Apply the product rule to $4 x^{5}$ .

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

Simplify the numerator.

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

$\frac{16 {(x^{5})}^{2}}{{(y^{4})}^{2}}$

Multiply the exponents in ${(x^{5})}^{2}$ .

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

$\frac{16 x^{5 \cdot 2}}{{(y^{4})}^{2}}$

Multiply $5$ by $2$ .

$\frac{16 x^{10}}{{(y^{4})}^{2}}$

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

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

$\frac{16 x^{10}}{y^{4 \cdot 2}}$

Multiply $4$ by $2$ .

$\frac{16 x^{10}}{y^{8}}$