Simplify (8x^-4y^-8)/(-2xy^5)

$\frac{8 x^{- 4} y^{- 8}}{- 2 x y^{5}}$

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

$\frac{8 y^{- 8}}{- 2 x y^{5} x^{4}}$

Move $y^{- 8}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{8}{- 2 x y^{5} x^{4} y^{8}}$

Simplify the denominator.

Multiply $x$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

$\frac{8}{- 2 (x^{4} x) y^{5} y^{8}}$

Multiply $x^{4}$ by $x$ .

Raise $x$ to the power of $1$ .

$\frac{8}{- 2 (x^{4} x^{1}) y^{5} y^{8}}$

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

$\frac{8}{- 2 x^{4 + 1} y^{5} y^{8}}$

Add $4$ and $1$ .

$\frac{8}{- 2 x^{5} y^{5} y^{8}}$

Multiply $y^{5}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

$\frac{8}{- 2 x^{5} (y^{8} y^{5})}$

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

$\frac{8}{- 2 x^{5} y^{8 + 5}}$

Add $8$ and $5$ .

$\frac{8}{- 2 x^{5} y^{13}}$

Cancel the common factor of $8$ and $- 2$ .

Factor $2$ out of $8$ .

$\frac{2 (4)}{- 2 x^{5} y^{13}}$

Cancel the common factors.

Factor $2$ out of $- 2 x^{5} y^{13}$ .

$\frac{2 (4)}{2 (- x^{5} y^{13})}$

Cancel the common factor.

$\frac{2 \cdot 4}{2 (- x^{5} y^{13})}$

Rewrite the expression.

$\frac{4}{- x^{5} y^{13}}$

Move the negative in front of the fraction.

$- \frac{4}{x^{5} y^{13}}$