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

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

Step 1

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

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

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

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

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

Step 3

Simplify the numerator.

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

$\frac{16 {(y^{3})}^{2}}{x^{2}}$

Multiply the exponents in ${(y^{3})}^{2}$ .

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

$\frac{16 y^{3 \cdot 2}}{x^{2}}$

Multiply $3$ by $2$ .

$\frac{16 y^{6}}{x^{2}}$