Simplify ((-4)^2m^4n^-7)/((-2)^-2q^5r^-3)

$\frac{{(- 4)}^{2} m^{4} n^{- 7}}{{(- 2)}^{- 2} q^{5} r^{- 3}}$

Simplify.

Move $n^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{{(- 4)}^{2} m^{4}}{{(- 2)}^{- 2} q^{5} r^{- 3} n^{7}}$

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

$\frac{{(- 4)}^{2} m^{4} {(- 2)}^{2}}{q^{5} r^{- 3} n^{7}}$

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

$\frac{{(- 4)}^{2} m^{4} {(- 2)}^{2} r^{3}}{q^{5} n^{7}}$

Simplify the numerator.

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

$\frac{16 m^{4} {(- 2)}^{2} r^{3}}{q^{5} n^{7}}$

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

$\frac{16 m^{4} \cdot 4 r^{3}}{q^{5} n^{7}}$

Multiply $4$ by $16$ .

$\frac{64 m^{4} r^{3}}{q^{5} n^{7}}$