Simplify (2x^4y^-3)^-1

${(2 x^{4} y^{- 3})}^{- 1}$

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

${(2 x^{4} \frac{1}{y^{3}})}^{- 1}$

Multiply $2 x^{4} \frac{1}{y^{3}}$ .

Combine $2$ and $\frac{1}{y^{3}}$ .

${(x^{4} \frac{2}{y^{3}})}^{- 1}$

Combine $x^{4}$ and $\frac{2}{y^{3}}$ .

${(\frac{x^{4} \cdot 2}{y^{3}})}^{- 1}$

Move $2$ to the left of $x^{4}$ .

${(\frac{2 \cdot x^{4}}{y^{3}})}^{- 1}$

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{y^{3}}{2 x^{4}}$