Simplify (6^-4)/((6^6)^-1)

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

Simplify the expression.

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

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

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

$\frac{6^{6}}{6^{4}}$

Cancel the common factor of $6^{6}$ and $6^{4}$ .

Factor $6^{4}$ out of $6^{6}$ .

$\frac{6^{4} \cdot 6^{2}}{6^{4}}$

Cancel the common factors.

Multiply by $1$ .

$\frac{6^{4} \cdot 6^{2}}{6^{4} \cdot 1}$

Cancel the common factor.

$\frac{6^{4} \cdot 6^{2}}{6^{4} \cdot 1}$

Rewrite the expression.

$\frac{6^{2}}{1}$

Divide $6^{2}$ by $1$ .

$6^{2}$

Raise $6$ to the power of $2$ .

$36$