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

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

Step 1

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

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

Step 2

Simplify the denominator.

Multiply $x^{2}$ by $x^{- 2}$ by adding the exponents.

Move $x^{- 2}$ .

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

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $- 2$ and $2$ .

$\frac{1}{3 x^{0} \cdot 3}$

Simplify $3 x^{0} \cdot 3$ .

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

Step 3

Multiply $3$ by $3$ .

$\frac{1}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$