Simplify (-2a^2b^4)/(4ab^-8)

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

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

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

Multiply $b^{4}$ by $b^{8}$ by adding the exponents.

Move $b^{8}$ .

$\frac{- 2 a^{2} (b^{8} b^{4})}{4 a}$

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

$\frac{- 2 a^{2} b^{8 + 4}}{4 a}$

Add $8$ and $4$ .

$\frac{- 2 a^{2} b^{12}}{4 a}$

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 a^{2} b^{12}$ .

$\frac{2 (- a^{2} b^{12})}{4 a}$

Cancel the common factors.

Factor $2$ out of $4 a$ .

$\frac{2 (- a^{2} b^{12})}{2 (2 a)}$

Cancel the common factor.

$\frac{2 (- a^{2} b^{12})}{2 (2 a)}$

Rewrite the expression.

$\frac{- a^{2} b^{12}}{2 a}$

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

Factor $a$ out of $- a^{2} b^{12}$ .

$\frac{a (- a b^{12})}{2 a}$

Cancel the common factors.

Factor $a$ out of $2 a$ .

$\frac{a (- a b^{12})}{a \cdot 2}$

Cancel the common factor.

$\frac{a (- a b^{12})}{a \cdot 2}$

Rewrite the expression.

$\frac{- a b^{12}}{2}$

Move the negative in front of the fraction.

$- \frac{a b^{12}}{2}$