Simplify ((-6)^-4)/(3^-2)

$\frac{{(- 6)}^{- 4}}{3^{- 2}}$

Step 1

Simplify the expression.

Move ${(- 6)}^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{- 2} {(- 6)}^{4}}$

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

$\frac{3^{2}}{{(- 6)}^{4}}$

Raise $3$ to the power of $2$ .

$\frac{9}{{(- 6)}^{4}}$

Raise $- 6$ to the power of $4$ .

$\frac{9}{1296}$

Step 2

Cancel the common factor of $9$ and $1296$ .

Factor $9$ out of $9$ .

$\frac{9 (1)}{1296}$

Cancel the common factors.

Factor $9$ out of $1296$ .

$\frac{9 \cdot 1}{9 \cdot 144}$

Cancel the common factor.

$\frac{9 \cdot 1}{9 \cdot 144}$

Rewrite the expression.

$\frac{1}{144}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{144}$

Decimal Form:

$0.0069\overline{4}$