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

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

Simplify.

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

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

Move ${(3 y)}^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Simplify the numerator.

Apply the product rule to $3 y$ .

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

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

$\frac{4 \cdot 27 y^{3}}{x^{2}}$

Multiply $4$ by $27$ .

$\frac{108 y^{3}}{x^{2}}$