Evaluate (-11x^3y)^-2

${(- 11 x^{3} y)}^{- 2}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{{(- 11 x^{3} y)}^{2}}$

Simplify the denominator.

Apply the product rule to $- 11 x^{3} y$ .

$\frac{1}{{(- 11 x^{3})}^{2} y^{2}}$

Apply the product rule to $- 11 x^{3}$ .

$\frac{1}{{(- 11)}^{2} {(x^{3})}^{2} y^{2}}$

Raise $- 11$ to the power of $2$ .

$\frac{1}{121 {(x^{3})}^{2} y^{2}}$

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

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

$\frac{1}{121 x^{3 \cdot 2} y^{2}}$

Multiply $3$ by $2$ .

$\frac{1}{121 x^{6} y^{2}}$