Simplify ((3a^-2y)/(x^3))^-2

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

Move $a^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

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

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

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

Apply the product rule to $\frac{x^{3} a^{2}}{3 y}$ .

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

Apply the product rule to $x^{3} a^{2}$ .

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

Apply the product rule to $3 y$ .

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

Simplify the numerator.

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

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

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

Multiply $3$ by $2$ .

$\frac{x^{6} {(a^{2})}^{2}}{3^{2} y^{2}}$

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

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

$\frac{x^{6} a^{2 \cdot 2}}{3^{2} y^{2}}$

Multiply $2$ by $2$ .

$\frac{x^{6} a^{4}}{3^{2} y^{2}}$

Raise $3$ to the power of $2$ .

$\frac{x^{6} a^{4}}{9 y^{2}}$