Simplify (-4a^-2b^4)/(8a^-6b^-3)

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

Step 1

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

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

Step 2

Move $b^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 3

Simplify the numerator.

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

Move $a^{6}$ .

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

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

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

Subtract $2$ from $6$ .

$\frac{- 4 a^{4} b^{4} b^{3}}{8}$

Multiply $b^{4}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$\frac{- 4 a^{4} (b^{3} b^{4})}{8}$

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

$\frac{- 4 a^{4} b^{3 + 4}}{8}$

Add $3$ and $4$ .

$\frac{- 4 a^{4} b^{7}}{8}$

Step 4

Cancel the common factor of $- 4$ and $8$ .

Factor $4$ out of $- 4 a^{4} b^{7}$ .

$\frac{4 (- a^{4} b^{7})}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$\frac{4 (- a^{4} b^{7})}{4 (2)}$

Cancel the common factor.

$\frac{4 (- a^{4} b^{7})}{4 \cdot 2}$

Rewrite the expression.

$\frac{- a^{4} b^{7}}{2}$

Step 5

Move the negative in front of the fraction.

$- \frac{a^{4} b^{7}}{2}$