Simplify -(20w^7)/(-4(w^-5)^3)

$- \frac{20 w^{7}}{- 4 {(w^{- 5})}^{3}}$

Cancel the common factor of $20$ and $- 4$ .

Factor $4$ out of $20 w^{7}$ .

$- \frac{4 (5 w^{7})}{- 4 {(w^{- 5})}^{3}}$

Cancel the common factors.

Factor $4$ out of $- 4 {(w^{- 5})}^{3}$ .

$- \frac{4 (5 w^{7})}{4 (- {(w^{- 5})}^{3})}$

Cancel the common factor.

$- \frac{4 (5 w^{7})}{4 (- {(w^{- 5})}^{3})}$

Rewrite the expression.

$- \frac{5 w^{7}}{- {(w^{- 5})}^{3}}$

Simplify the denominator.

Multiply the exponents in ${(w^{- 5})}^{3}$ .

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

$- \frac{5 w^{7}}{- w^{- 5 \cdot 3}}$

Multiply $- 5$ by $3$ .

$- \frac{5 w^{7}}{- w^{- 15}}$

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

$- \frac{5 w^{7}}{- \frac{1}{w^{15}}}$

Multiply the numerator by the reciprocal of the denominator.

$- (5 w^{7} (- w^{15}))$

Multiply $w^{7}$ by $w^{15}$ by adding the exponents.

Move $w^{15}$ .

$- (5 (w^{15} w^{7}) \cdot - 1)$

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

$- (5 w^{15 + 7} \cdot - 1)$

Add $15$ and $7$ .

$- (5 w^{22} \cdot - 1)$

Multiply $- 1$ by $5$ .

$- (- 5 w^{22})$

Multiply $- 5$ by $- 1$ .

$5 w^{22}$