Simplify ((2x^3)/(3x^2))^-1

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

Step 1

Cancel the common factor of $x^{3}$ and $x^{2}$ .

Factor $x^{2}$ out of $2 x^{3}$ .

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

Cancel the common factors.

Factor $x^{2}$ out of $3 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

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

$\frac{3}{2 x}$