Simplify ((4x^5y)/(-x^6y^3))^-2

${(\frac{4 x^{5} y}{- x^{6} y^{3}})}^{- 2}$

Cancel the common factor of $x^{5}$ and $x^{6}$ .

Factor $x^{5}$ out of $4 x^{5} y$ .

${(\frac{x^{5} (4 y)}{- x^{6} y^{3}})}^{- 2}$

Cancel the common factors.

Factor $x^{5}$ out of $- x^{6} y^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $y$ out of $4 y$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Change the sign of the exponent by rewriting the base as its reciprocal.

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

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

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

${(- 1)}^{2} {(\frac{x y^{2}}{4})}^{2}$

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

${(- 1)}^{2} \frac{{(x y^{2})}^{2}}{4^{2}}$

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

${(- 1)}^{2} \frac{x^{2} {(y^{2})}^{2}}{4^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{x^{2} {(y^{2})}^{2}}{4^{2}}$

Multiply $\frac{x^{2} {(y^{2})}^{2}}{4^{2}}$ by $1$ .

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

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

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

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

Multiply $2$ by $2$ .

$\frac{x^{2} y^{4}}{4^{2}}$

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

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