Simplify (20(mn)^-3)/(-5m^2n^2)

$\frac{20 {(m n)}^{- 3}}{- 5 m^{2} n^{2}}$

Reduce the expression by cancelling the common factors.

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

$\frac{20}{- 5 m^{2} n^{2} {(m n)}^{3}}$

Cancel the common factor of $20$ and $- 5$ .

Factor $5$ out of $20$ .

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

Cancel the common factors.

Factor $5$ out of $- 5 m^{2} n^{2} {(m n)}^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the denominator.

Apply the product rule to $m n$ .

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

Combine exponents.

Multiply $m^{2}$ by $m^{3}$ by adding the exponents.

Move $m^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Multiply $n^{2}$ by $n^{3}$ by adding the exponents.

Move $n^{3}$ .

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

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

$\frac{4}{- m^{5} n^{3 + 2}}$

Add $3$ and $2$ .

$\frac{4}{- m^{5} n^{5}}$

Move the negative in front of the fraction.

$- \frac{4}{m^{5} n^{5}}$