Simplify ((-8)^-2)/(3^-4)

$\frac{{(- 8)}^{- 2}}{3^{- 4}}$

Move ${(- 8)}^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{- 4} {(- 8)}^{2}}$

Move $3^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3^{4}}{{(- 8)}^{2}}$

Raise $3$ to the power of $4$ .

$\frac{81}{{(- 8)}^{2}}$

Raise $- 8$ to the power of $2$ .

$\frac{81}{64}$

The result can be shown in multiple forms.

Exact Form:

$\frac{81}{64}$

Decimal Form:

$1.265625$

Mixed Number Form:

$1 \frac{17}{64}$