Simplify (-16a^-3b^-5)/(2a^-4b^2)

$\frac{- 16 a^{- 3} b^{- 5}}{2 a^{- 4} b^{2}}$

Step 1

Move $b^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 16 a^{- 3}}{2 a^{- 4} b^{2} b^{5}}$

Step 2

Multiply $b^{2}$ by $b^{5}$ by adding the exponents.

Move $b^{5}$ .

$\frac{- 16 a^{- 3}}{2 a^{- 4} (b^{5} b^{2})}$

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

$\frac{- 16 a^{- 3}}{2 a^{- 4} b^{5 + 2}}$

Add $5$ and $2$ .

$\frac{- 16 a^{- 3}}{2 a^{- 4} b^{7}}$

Step 3

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

$\frac{- 16 a^{- 3} a^{4}}{2 b^{7}}$

Step 4

Simplify the numerator.

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

Move $a^{4}$ .

$\frac{- 16 (a^{4} a^{- 3})}{2 b^{7}}$

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

$\frac{- 16 a^{4 - 3}}{2 b^{7}}$

Subtract $3$ from $4$ .

$\frac{- 16 a^{1}}{2 b^{7}}$

Simplify $- 16 a^{1}$ .

$\frac{- 16 a}{2 b^{7}}$

Step 5

Cancel the common factor of $- 16$ and $2$ .

Factor $2$ out of $- 16 a$ .

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

Cancel the common factors.

Factor $2$ out of $2 b^{7}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

Move the negative in front of the fraction.

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