Evaluate (x^-3)(3x^-2)^-1

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

$\frac{1}{x^{3}} \cdot \frac{x^{2}}{3}$

Step 5

Combine.

$\frac{1 x^{2}}{x^{3} \cdot 3}$

Step 6

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

Factor $x^{2}$ out of $1 x^{2}$ .

$\frac{x^{2} \cdot 1}{x^{3} \cdot 3}$

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{x \cdot 3}$

Step 7

Move $3$ to the left of $x$ .

$\frac{1}{3 x}$