Simplify (6x^3)(3xy)^-1

$(6 x^{3}) {(3 x y)}^{- 1}$

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

$6 x^{3} \frac{1}{3 x y}$

Cancel the common factor of $3 x$ .

Factor $3 x$ out of $6 x^{3}$ .

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

Factor $3 x$ out of $3 x y$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 x^{2} \frac{1}{y}$

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

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

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

$\frac{x^{2} \cdot 2}{y}$

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

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