Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Move $a^{6}$ .

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

Step 3.1.2

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

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

Step 3.1.3

Subtract $2$ from $6$ .

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

Step 3.2

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

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Step 3.2.1

Move $b^{4}$ .

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

Step 3.2.2

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

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

Step 3.2.3

Subtract $3$ from $4$ .

$\frac{8}{a^{4} b^{1}}$

Step 3.3

Simplify $a^{4} b^{1}$ .

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