Simplify (3^-1)/((3^2)^-6)

$\frac{3^{- 1}}{{(3^{2})}^{- 6}}$

Simplify the expression.

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

$\frac{1}{{(3^{2})}^{- 6} \cdot 3}$

Move ${(3^{2})}^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{{(3^{2})}^{6}}{3}$

Simplify the numerator.

Multiply the exponents in ${(3^{2})}^{6}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{3^{2 \cdot 6}}{3}$

Multiply $2$ by $6$ .

$\frac{3^{12}}{3}$

Raise $3$ to the power of $12$ .

$\frac{531441}{3}$

Divide $531441$ by $3$ .

$177147$