Write the Fraction in Simplest Form ((6^-4)^-9)/(6^6)

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

Step 1

Move ${(6^{- 4})}^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{6^{6} {(6^{- 4})}^{9}}$

Step 2

Simplify the denominator.

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

$\frac{1}{46656 {(6^{- 4})}^{9}}$

Multiply the exponents in ${(6^{- 4})}^{9}$ .

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

$\frac{1}{46656 \cdot 6^{- 4 \cdot 9}}$

Multiply $- 4$ by $9$ .

$\frac{1}{46656 \cdot 6^{- 36}}$

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

$\frac{1}{46656 \frac{1}{6^{36}}}$

Raise $6$ to the power of $36$ .

$\frac{1}{46656 (\frac{1}{10314424798490500000000000000})}$

Step 3

Combine $46656$ and $\frac{1}{10314424798490500000000000000}$ .

$\frac{1}{\frac{46656}{10314424798490500000000000000}}$

Step 4

Cancel the common factor of $46656$ and $10314424798490500000000000000$ .

Factor $64$ out of $46656$ .

$\frac{1}{\frac{64 (729)}{10314424798490500000000000000}}$

Cancel the common factors.

Factor $64$ out of $10314424798490500000000000000$ .

$\frac{1}{\frac{64 \cdot 729}{64 \cdot 161162887476414062500000000}}$

Cancel the common factor.

$\frac{1}{\frac{64 \cdot 729}{64 \cdot 161162887476414062500000000}}$

Rewrite the expression.

$\frac{1}{\frac{729}{161162887476414062500000000}}$

Step 5

Multiply the numerator by the reciprocal of the denominator.

$1 (\frac{161162887476414062500000000}{729})$

Step 6

Multiply $\frac{161162887476414062500000000}{729}$ by $1$ .

$\frac{161162887476414062500000000}{729}$