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

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

Step 1

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.

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

Step 2

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 $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Multiply the numerator by the reciprocal of the denominator.

$5 w^{7} w^{15}$

Step 4

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

Move $w^{15}$ .

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

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

$5 w^{15 + 7}$

Add $15$ and $7$ .

$5 w^{22}$