Basic Math Examples

$a^{- 2} b^{3} \div a^{4} b^{- 1}$

Step 1

Rewrite the division as a fraction.

$\frac{a^{- 2} b^{3}}{a^{4} b^{- 1}}$

Step 2

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

$\frac{b^{3}}{a^{4} b^{- 1} a^{2}}$

Step 3

Multiply $a^{4}$ by $a^{2}$ by adding the exponents.

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Step 3.1

Move $a^{2}$ .

$\frac{b^{3}}{a^{2} a^{4} b^{- 1}}$

Step 3.2

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

$\frac{b^{3}}{a^{2 + 4} b^{- 1}}$

Step 3.3

Add $2$ and $4$ .

$\frac{b^{3}}{a^{6} b^{- 1}}$

Step 4

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

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

Step 5

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

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Step 5.1

Multiply $b^{3}$ by $b$ .

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Step 5.1.1

Raise $b$ to the power of $1$ .

$\frac{b^{3} b^{1}}{a^{6}}$

Step 5.1.2

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

$\frac{b^{3 + 1}}{a^{6}}$

Step 5.2

Add $3$ and $1$ .

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