Simplify (27a^-6b^4c^8)/(9a^2b^-2c^8)

$\frac{27 a^{- 6} b^{4} c^{8}}{9 a^{2} b^{- 2} c^{8}}$

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

$\frac{27 b^{4} c^{8}}{9 a^{2} b^{- 2} c^{8} a^{6}}$

Multiply $a^{2}$ by $a^{6}$ by adding the exponents.

Move $a^{6}$ .

$\frac{27 b^{4} c^{8}}{9 (a^{6} a^{2}) b^{- 2} c^{8}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{27 b^{4} c^{8}}{9 a^{6 + 2} b^{- 2} c^{8}}$

Add $6$ and $2$ .

$\frac{27 b^{4} c^{8}}{9 a^{8} b^{- 2} c^{8}}$

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

$\frac{27 b^{4} c^{8} b^{2}}{9 a^{8} c^{8}}$

Multiply $b^{4}$ by $b^{2}$ by adding the exponents.

Move $b^{2}$ .

$\frac{27 (b^{2} b^{4}) c^{8}}{9 a^{8} c^{8}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{27 b^{2 + 4} c^{8}}{9 a^{8} c^{8}}$

Add $2$ and $4$ .

$\frac{27 b^{6} c^{8}}{9 a^{8} c^{8}}$

Cancel the common factor of $27$ and $9$ .

Factor $9$ out of $27 b^{6} c^{8}$ .

$\frac{9 (3 b^{6} c^{8})}{9 a^{8} c^{8}}$

Cancel the common factors.

Factor $9$ out of $9 a^{8} c^{8}$ .

$\frac{9 (3 b^{6} c^{8})}{9 (a^{8} c^{8})}$

Cancel the common factor.

$\frac{9 (3 b^{6} c^{8})}{9 (a^{8} c^{8})}$

Rewrite the expression.

$\frac{3 b^{6} c^{8}}{a^{8} c^{8}}$

Cancel the common factor of $c^{8}$ .

Cancel the common factor.

$\frac{3 b^{6} c^{8}}{a^{8} c^{8}}$

Rewrite the expression.

$\frac{3 b^{6}}{a^{8}}$