Precalculus Examples

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

Step 1

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

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

Step 2

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

$a^{- 3} b^{4} a^{6} b^{6}$

Step 3

Multiply $a^{- 3}$ by $a^{6}$ by adding the exponents.

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Step 3.1

Move $a^{6}$ .

$a^{6} a^{- 3} b^{4} b^{6}$

Step 3.2

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

$a^{6 - 3} b^{4} b^{6}$

Step 3.3

Subtract $3$ from $6$ .

$a^{3} b^{4} b^{6}$

Step 4

Multiply $b^{4}$ by $b^{6}$ by adding the exponents.

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Step 4.1

Move $b^{6}$ .

$a^{3} (b^{6} b^{4})$

Step 4.2

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

$a^{3} b^{6 + 4}$

Step 4.3

Add $6$ and $4$ .

$a^{3} b^{10}$