Simplify (-4(k^-3v^4)^-1)/(20k^-2v^8)

$\frac{- 4 {(k^{- 3} v^{4})}^{- 1}}{20 k^{- 2} v^{8}}$

Move ${(k^{- 3} v^{4})}^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 4}{20 k^{- 2} v^{8} (k^{- 3} v^{4})}$

Simplify the denominator.

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

Move $k^{- 3}$ .

$\frac{- 4}{20 (k^{- 3} k^{- 2}) v^{8} v^{4}}$

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

$\frac{- 4}{20 k^{- 3 - 2} v^{8} v^{4}}$

Subtract $2$ from $- 3$ .

$\frac{- 4}{20 k^{- 5} v^{8} v^{4}}$

Multiply $v^{8}$ by $v^{4}$ by adding the exponents.

Move $v^{4}$ .

$\frac{- 4}{20 k^{- 5} (v^{4} v^{8})}$

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

$\frac{- 4}{20 k^{- 5} v^{4 + 8}}$

Add $4$ and $8$ .

$\frac{- 4}{20 k^{- 5} v^{12}}$

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

$\frac{- 4 k^{5}}{20 v^{12}}$

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

Factor $4$ out of $- 4 k^{5}$ .

$\frac{4 (- k^{5})}{20 v^{12}}$

Cancel the common factors.

Factor $4$ out of $20 v^{12}$ .

$\frac{4 (- k^{5})}{4 (5 v^{12})}$

Cancel the common factor.

$\frac{4 (- k^{5})}{4 (5 v^{12})}$

Rewrite the expression.

$\frac{- k^{5}}{5 v^{12}}$

Move the negative in front of the fraction.

$- \frac{k^{5}}{5 v^{12}}$