Simplify ((3m^-5n^2)/(4m^-2n^0))^2

${(\frac{3 m^{- 5} n^{2}}{4 m^{- 2} n^{0}})}^{2}$

Move $m^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{3 n^{2}}{4 m^{- 2} n^{0} m^{5}})}^{2}$

Simplify the denominator.

Multiply $m^{- 2}$ by $m^{5}$ by adding the exponents.

Move $m^{5}$ .

${(\frac{3 n^{2}}{4 (m^{5} m^{- 2}) n^{0}})}^{2}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

${(\frac{3 n^{2}}{4 m^{5 - 2} n^{0}})}^{2}$

Subtract $2$ from $5$ .

${(\frac{3 n^{2}}{4 m^{3} n^{0}})}^{2}$

Simplify $4 m^{3} n^{0}$ .

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

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

Apply the product rule to $\frac{3 n^{2}}{4 m^{3}}$ .

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

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

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

Apply the product rule to $4 m^{3}$ .

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

Simplify the numerator.

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

$\frac{9 {(n^{2})}^{2}}{4^{2} {(m^{3})}^{2}}$

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

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

$\frac{9 n^{2 \cdot 2}}{4^{2} {(m^{3})}^{2}}$

Multiply $2$ by $2$ .

$\frac{9 n^{4}}{4^{2} {(m^{3})}^{2}}$

Simplify the denominator.

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

$\frac{9 n^{4}}{16 {(m^{3})}^{2}}$

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

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

$\frac{9 n^{4}}{16 m^{3 \cdot 2}}$

Multiply $3$ by $2$ .

$\frac{9 n^{4}}{16 m^{6}}$