Simplify (-5m^-5)/(-3(m^-5)^4)

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

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

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

Simplify the denominator.

Multiply the exponents in ${(m^{- 5})}^{4}$ .

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

$\frac{- 5}{- 3 m^{- 5 \cdot 4} m^{5}}$

Multiply $- 5$ by $4$ .

$\frac{- 5}{- 3 m^{- 20} m^{5}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 5}{- 3 \frac{1}{m^{20}} m^{5}}$

Combine exponents.

Combine $- 3$ and $\frac{1}{m^{20}}$ .

$\frac{- 5}{\frac{- 3}{m^{20}} m^{5}}$

Combine $\frac{- 3}{m^{20}}$ and $m^{5}$ .

$\frac{- 5}{\frac{- 3 m^{5}}{m^{20}}}$

Reduce the expression $\frac{- 3 m^{5}}{m^{20}}$ by cancelling the common factors.

Factor $m^{5}$ out of $- 3 m^{5}$ .

$\frac{- 5}{\frac{m^{5} \cdot - 3}{m^{20}}}$

Factor $m^{5}$ out of $m^{20}$ .

$\frac{- 5}{\frac{m^{5} \cdot - 3}{m^{5} m^{15}}}$

Cancel the common factor.

$\frac{- 5}{\frac{m^{5} \cdot - 3}{m^{5} m^{15}}}$

Rewrite the expression.

$\frac{- 5}{\frac{- 3}{m^{15}}}$

Move the negative in front of the fraction.

$\frac{- 5}{- \frac{3}{m^{15}}}$

Multiply the numerator by the reciprocal of the denominator.

$- 5 (- \frac{m^{15}}{3})$

Multiply $- 5 (- \frac{m^{15}}{3})$ .

Multiply $- 1$ by $- 5$ .

$5 \frac{m^{15}}{3}$

Combine $5$ and $\frac{m^{15}}{3}$ .

$\frac{5 m^{15}}{3}$