Simplify (-64a^15a^-7b^-3)/(-8a^2b^-3)

$\frac{- 64 a^{15} a^{- 7} b^{- 3}}{- 8 a^{2} b^{- 3}}$

Multiply $a^{15}$ by $a^{- 7}$ by adding the exponents.

Move $a^{- 7}$ .

$\frac{- 64 (a^{- 7} a^{15}) b^{- 3}}{- 8 a^{2} b^{- 3}}$

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

$\frac{- 64 a^{- 7 + 15} b^{- 3}}{- 8 a^{2} b^{- 3}}$

Add $- 7$ and $15$ .

$\frac{- 64 a^{8} b^{- 3}}{- 8 a^{2} b^{- 3}}$

Cancel the common factor of $- 64$ and $- 8$ .

Factor $- 8$ out of $- 64 a^{8} b^{- 3}$ .

$\frac{- 8 (8 a^{8} b^{- 3})}{- 8 a^{2} b^{- 3}}$

Cancel the common factors.

Factor $- 8$ out of $- 8 a^{2} b^{- 3}$ .

$\frac{- 8 (8 a^{8} b^{- 3})}{- 8 (a^{2} b^{- 3})}$

Cancel the common factor.

$\frac{- 8 (8 a^{8} b^{- 3})}{- 8 (a^{2} b^{- 3})}$

Rewrite the expression.

$\frac{8 a^{8} b^{- 3}}{a^{2} b^{- 3}}$

Cancel the common factor of $a^{8}$ and $a^{2}$ .

Factor $a^{2}$ out of $8 a^{8} b^{- 3}$ .

$\frac{a^{2} (8 a^{6} b^{- 3})}{a^{2} b^{- 3}}$

Cancel the common factors.

Factor $a^{2}$ out of $a^{2} b^{- 3}$ .

$\frac{a^{2} (8 a^{6} b^{- 3})}{a^{2} (b^{- 3})}$

Cancel the common factor.

$\frac{a^{2} (8 a^{6} b^{- 3})}{a^{2} b^{- 3}}$

Rewrite the expression.

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

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

Cancel the common factor.

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

Divide $8 a^{6}$ by $1$ .

$8 a^{6}$