Basic Math Examples

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

Step 1

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

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

Step 2

Simplify the denominator.

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Step 2.1

Multiply $b^{- 2}$ by $b^{3}$ by adding the exponents.

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Step 2.1.1

Move $b^{3}$ .

$\frac{a^{4}}{a (b^{3} b^{- 2})}$

Step 2.1.2

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

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

Step 2.1.3

Subtract $2$ from $3$ .

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

Step 2.2

Simplify $a b^{1}$ .

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

Step 3

Cancel the common factor of $a^{4}$ and $a$ .

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Step 3.1

Factor $a$ out of $a^{4}$ .

$\frac{a \cdot a^{3}}{a b}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a$ out of $a b$ .

$\frac{a \cdot a^{3}}{a (b)}$

Step 3.2.2

Cancel the common factor.

$\frac{a \cdot a^{3}}{a b}$

Step 3.2.3

Rewrite the expression.

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