Basic Math Examples

$\frac{\frac{6 q^{2}}{5 π}}{\frac{9 π}{20 q}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 q^{2}}{5 π} \cdot \frac{20 q}{9 π}$

Step 2

Combine.

$\frac{6 q^{2} (20 q)}{5 π (9 π)}$

Step 3

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

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Step 3.1

Move $q$ .

$\frac{6 (q \cdot q^{2}) \cdot 20}{5 π (9 π)}$

Step 3.2

Multiply $q$ by $q^{2}$ .

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Step 3.2.1

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

$\frac{6 (q^{1} q^{2}) \cdot 20}{5 π (9 π)}$

Step 3.2.2

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

$\frac{6 q^{1 + 2} \cdot 20}{5 π (9 π)}$

Step 3.3

Add $1$ and $2$ .

$\frac{6 q^{3} \cdot 20}{5 π (9 π)}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $6$ and $9$ .

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Step 4.1.1

Factor $3$ out of $6 q^{3} \cdot 20$ .

$\frac{3 (2 q^{3} \cdot 20)}{5 π (9 π)}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $3$ out of $5 π (9 π)$ .

$\frac{3 (2 q^{3} \cdot 20)}{3 (5 π (3 π))}$

Step 4.1.2.2

Cancel the common factor.

$\frac{3 (2 q^{3} \cdot 20)}{3 (5 π (3 π))}$

Step 4.1.2.3

Rewrite the expression.

$\frac{2 q^{3} \cdot 20}{5 π (3 π)}$

Step 4.2

Cancel the common factor of $20$ and $5$ .

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Step 4.2.1

Factor $5$ out of $2 q^{3} \cdot 20$ .

$\frac{5 (2 q^{3} \cdot 4)}{5 π (3 π)}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Factor $5$ out of $5 π (3 π)$ .

$\frac{5 (2 q^{3} \cdot 4)}{5 (π (3 π))}$

Step 4.2.2.2

Cancel the common factor.

$\frac{5 (2 q^{3} \cdot 4)}{5 (π (3 π))}$

Step 4.2.2.3

Rewrite the expression.

$\frac{2 q^{3} \cdot 4}{π (3 π)}$

Step 4.3

Multiply $4$ by $2$ .

$\frac{8 q^{3}}{π \cdot 3 π}$

Step 5

Simplify the denominator.

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Step 5.1

Raise $π$ to the power of $1$ .

$\frac{8 q^{3}}{3 (π^{1} π)}$

Step 5.2

Raise $π$ to the power of $1$ .

$\frac{8 q^{3}}{3 (π^{1} π^{1})}$

Step 5.3

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

$\frac{8 q^{3}}{3 π^{1 + 1}}$

Step 5.4

Add $1$ and $1$ .

$\frac{8 q^{3}}{3 π^{2}}$