Basic Math Examples

$\frac{a^{6} b^{- 3}}{{(a b)}^{- 2}}$

Step 1

Simplify.

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Step 1.1

Move $b^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{a^{6}}{{(a b)}^{- 2} b^{3}}$

Step 1.2

Move ${(a b)}^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{6} {(a b)}^{2}}{b^{3}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $a b$ .

$\frac{a^{6} a^{2} b^{2}}{b^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{a^{6 + 2} b^{2}}{b^{3}}$

Step 2.2.2

Add $6$ and $2$ .

$\frac{a^{8} b^{2}}{b^{3}}$

Step 3

Cancel the common factor of $b^{2}$ and $b^{3}$ .

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Step 3.1

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

$\frac{b^{2} a^{8}}{b^{3}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $b^{2}$ out of $b^{3}$ .

$\frac{b^{2} a^{8}}{b^{2} b}$

Step 3.2.2

Cancel the common factor.

$\frac{b^{2} a^{8}}{b^{2} b}$

Step 3.2.3

Rewrite the expression.

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