Simplify (-20a^-2b^-7)/(5a^-5b^3)

$\frac{- 20 a^{- 2} b^{- 7}}{5 a^{- 5} b^{3}}$

Step 1

Move $b^{- 7}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 20 a^{- 2}}{5 a^{- 5} b^{3} b^{7}}$

Step 2

Multiply $b^{3}$ by $b^{7}$ by adding the exponents.

Move $b^{7}$ .

$\frac{- 20 a^{- 2}}{5 a^{- 5} (b^{7} b^{3})}$

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

$\frac{- 20 a^{- 2}}{5 a^{- 5} b^{7 + 3}}$

Add $7$ and $3$ .

$\frac{- 20 a^{- 2}}{5 a^{- 5} b^{10}}$

Step 3

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

$\frac{- 20 a^{- 2} a^{5}}{5 b^{10}}$

Step 4

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

Move $a^{5}$ .

$\frac{- 20 (a^{5} a^{- 2})}{5 b^{10}}$

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

$\frac{- 20 a^{5 - 2}}{5 b^{10}}$

Subtract $2$ from $5$ .

$\frac{- 20 a^{3}}{5 b^{10}}$

Step 5

Cancel the common factor of $- 20$ and $5$ .

Factor $5$ out of $- 20 a^{3}$ .

$\frac{5 (- 4 a^{3})}{5 b^{10}}$

Cancel the common factors.

Factor $5$ out of $5 b^{10}$ .

$\frac{5 (- 4 a^{3})}{5 (b^{10})}$

Cancel the common factor.

$\frac{5 (- 4 a^{3})}{5 b^{10}}$

Rewrite the expression.

$\frac{- 4 a^{3}}{b^{10}}$

Step 6

Move the negative in front of the fraction.

$- \frac{4 a^{3}}{b^{10}}$