Simplify ((3x^-1)/(4y^-1))^-2

${(\frac{3 x^{- 1}}{4 y^{- 1}})}^{- 2}$

Step 1

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

${(\frac{3}{4 y^{- 1} x})}^{- 2}$

Step 2

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

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

Step 3

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

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

Step 4

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

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

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

Apply the product rule to $4 x$ .

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

Apply the product rule to $3 y$ .

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

Step 5

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

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

Step 6

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

$\frac{16 x^{2}}{9 y^{2}}$