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

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

Step 1

Simplify the expression.

Move ${(3 x)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Move ${(x^{3})}^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 2

Simplify the denominator.

Apply the product rule to $3 x$ .

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

Raise $3$ to the power of $2$ .

$\frac{x^{3}}{9 x^{2}}$

Step 3

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

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

$\frac{x^{2} x}{9 x^{2}}$

Cancel the common factors.

Factor $x^{2}$ out of $9 x^{2}$ .

$\frac{x^{2} x}{x^{2} \cdot 9}$

Cancel the common factor.

$\frac{x^{2} x}{x^{2} \cdot 9}$

Rewrite the expression.

$\frac{x}{9}$