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

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

Step 1

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

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

Step 2

Multiply $3^{- 1}$ by $3^{2}$ by adding the exponents.

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

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

Add $- 1$ and $2$ .

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

Step 3

Simplify $3^{1}$ .

$3^{- 1}$

Step 4

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

$\frac{1}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$