Simplify (((3mn)/2)^-1)^-4

${({(\frac{3 m n}{2})}^{- 1})}^{- 4}$

Step 1

Multiply the exponents in ${({(\frac{3 m n}{2})}^{- 1})}^{- 4}$ .

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

${(\frac{3 m n}{2})}^{- - 4}$

Multiply $- 1$ by $- 4$ .

${(\frac{3 m n}{2})}^{4}$

Step 2

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

Apply the product rule to $\frac{3 m n}{2}$ .

$\frac{{(3 m n)}^{4}}{2^{4}}$

Apply the product rule to $3 m n$ .

$\frac{{(3 m)}^{4} n^{4}}{2^{4}}$

Apply the product rule to $3 m$ .

$\frac{3^{4} m^{4} n^{4}}{2^{4}}$

Step 3

Raise $3$ to the power of $4$ .

$\frac{81 m^{4} n^{4}}{2^{4}}$

Step 4

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

$\frac{81 m^{4} n^{4}}{16}$