Simplify (-8a^8b^-2)/(10a^-4b^-10)

$\frac{- 8 a^{8} b^{- 2}}{10 a^{- 4} b^{- 10}}$

Step 1

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

$\frac{- 8 a^{8} b^{- 2} a^{4}}{10 b^{- 10}}$

Step 2

Move $b^{- 10}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{- 8 a^{8} b^{- 2} a^{4} b^{10}}{10}$

Step 3

Simplify the numerator.

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

Move $a^{4}$ .

$\frac{- 8 (a^{4} a^{8}) b^{- 2} b^{10}}{10}$

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

$\frac{- 8 a^{4 + 8} b^{- 2} b^{10}}{10}$

Add $4$ and $8$ .

$\frac{- 8 a^{12} b^{- 2} b^{10}}{10}$

Multiply $b^{- 2}$ by $b^{10}$ by adding the exponents.

Move $b^{10}$ .

$\frac{- 8 a^{12} (b^{10} b^{- 2})}{10}$

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

$\frac{- 8 a^{12} b^{10 - 2}}{10}$

Subtract $2$ from $10$ .

$\frac{- 8 a^{12} b^{8}}{10}$

Step 4

Cancel the common factor of $- 8$ and $10$ .

Factor $2$ out of $- 8 a^{12} b^{8}$ .

$\frac{2 (- 4 a^{12} b^{8})}{10}$

Cancel the common factors.

Factor $2$ out of $10$ .

$\frac{2 (- 4 a^{12} b^{8})}{2 (5)}$

Cancel the common factor.

$\frac{2 (- 4 a^{12} b^{8})}{2 \cdot 5}$

Rewrite the expression.

$\frac{- 4 a^{12} b^{8}}{5}$

Step 5

Move the negative in front of the fraction.

$- \frac{4 a^{12} b^{8}}{5}$