Basic Math Examples

$3^{2} q^{- 3} \div 2^{3} q^{- 2}$

Step 1

Rewrite the division as a fraction.

$\frac{3^{2} q^{- 3}}{2^{3} q^{- 2}}$

Step 2

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

$\frac{3^{2}}{2^{3} q^{- 2} q^{3}}$

Step 3

Simplify the denominator.

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Step 3.1

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

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Step 3.1.1

Move $q^{3}$ .

$\frac{3^{2}}{2^{3} (q^{3} q^{- 2})}$

Step 3.1.2

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

$\frac{3^{2}}{2^{3} q^{3 - 2}}$

Step 3.1.3

Subtract $2$ from $3$ .

$\frac{3^{2}}{2^{3} q^{1}}$

Step 3.2

Simplify $2^{3} q^{1}$ .

$\frac{3^{2}}{2^{3} q}$

Step 4

Raise $3$ to the power of $2$ .

$\frac{9}{2^{3} q}$

Step 5

Raise $2$ to the power of $3$ .

$\frac{9}{8 q}$