Evaluate (14a^4b^6c^-10)/(8a^-2b^3c^-5)

$\frac{14 a^{4} b^{6} c^{- 10}}{8 a^{- 2} b^{3} c^{- 5}}$

Move $c^{- 10}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{14 a^{4} b^{6}}{8 a^{- 2} b^{3} c^{- 5} c^{10}}$

Multiply $c^{- 5}$ by $c^{10}$ by adding the exponents.

Move $c^{10}$ .

$\frac{14 a^{4} b^{6}}{8 a^{- 2} b^{3} (c^{10} c^{- 5})}$

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

$\frac{14 a^{4} b^{6}}{8 a^{- 2} b^{3} c^{10 - 5}}$

Subtract $5$ from $10$ .

$\frac{14 a^{4} b^{6}}{8 a^{- 2} b^{3} c^{5}}$

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

$\frac{14 a^{4} b^{6} a^{2}}{8 b^{3} c^{5}}$

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

Move $a^{2}$ .

$\frac{14 (a^{2} a^{4}) b^{6}}{8 b^{3} c^{5}}$

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

$\frac{14 a^{2 + 4} b^{6}}{8 b^{3} c^{5}}$

Add $2$ and $4$ .

$\frac{14 a^{6} b^{6}}{8 b^{3} c^{5}}$

Cancel the common factor of $14$ and $8$ .

Factor $2$ out of $14 a^{6} b^{6}$ .

$\frac{2 (7 a^{6} b^{6})}{8 b^{3} c^{5}}$

Cancel the common factors.

Factor $2$ out of $8 b^{3} c^{5}$ .

$\frac{2 (7 a^{6} b^{6})}{2 (4 b^{3} c^{5})}$

Cancel the common factor.

$\frac{2 (7 a^{6} b^{6})}{2 (4 b^{3} c^{5})}$

Rewrite the expression.

$\frac{7 a^{6} b^{6}}{4 b^{3} c^{5}}$

Cancel the common factor of $b^{6}$ and $b^{3}$ .

Factor $b^{3}$ out of $7 a^{6} b^{6}$ .

$\frac{b^{3} (7 a^{6} b^{3})}{4 b^{3} c^{5}}$

Cancel the common factors.

Factor $b^{3}$ out of $4 b^{3} c^{5}$ .

$\frac{b^{3} (7 a^{6} b^{3})}{b^{3} (4 c^{5})}$

Cancel the common factor.

$\frac{b^{3} (7 a^{6} b^{3})}{b^{3} (4 c^{5})}$

Rewrite the expression.

$\frac{7 a^{6} b^{3}}{4 c^{5}}$