Basic Math Examples

$\frac{8 m^{5} n}{5 π^{2}} \cdot \frac{15 m π}{24 m^{2} n^{4}}$

Step 1

Combine.

$\frac{8 m^{5} n (15 m π)}{5 π^{2} (24 m^{2} n^{4})}$

Step 2

Multiply $m^{5}$ by $m$ by adding the exponents.

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Step 2.1

Move $m$ .

$\frac{8 (m \cdot m^{5}) n (15 π)}{5 π^{2} (24 m^{2} n^{4})}$

Step 2.2

Multiply $m$ by $m^{5}$ .

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Step 2.2.1

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

$\frac{8 (m^{1} m^{5}) n (15 π)}{5 π^{2} (24 m^{2} n^{4})}$

Step 2.2.2

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

$\frac{8 m^{1 + 5} n (15 π)}{5 π^{2} (24 m^{2} n^{4})}$

Step 2.3

Add $1$ and $5$ .

$\frac{8 m^{6} n (15 π)}{5 π^{2} (24 m^{2} n^{4})}$

Step 3

Cancel the common factor of $8$ and $24$ .

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Step 3.1

Factor $8$ out of $8 m^{6} n (15 π)$ .

$\frac{8 (m^{6} n (15 π))}{5 π^{2} (24 m^{2} n^{4})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $8$ out of $5 π^{2} (24 m^{2} n^{4})$ .

$\frac{8 (m^{6} n (15 π))}{8 (5 π^{2} (3 m^{2} n^{4}))}$

Step 3.2.2

Cancel the common factor.

$\frac{8 (m^{6} n (15 π))}{8 (5 π^{2} (3 m^{2} n^{4}))}$

Step 3.2.3

Rewrite the expression.

$\frac{m^{6} n (15 π)}{5 π^{2} (3 m^{2} n^{4})}$

Step 4

Cancel the common factor of $m^{6}$ and $m^{2}$ .

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Step 4.1

Factor $m^{2}$ out of $m^{6} n (15 π)$ .

$\frac{m^{2} (m^{4} n (15 π))}{5 π^{2} (3 m^{2} n^{4})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $m^{2}$ out of $5 π^{2} (3 m^{2} n^{4})$ .

$\frac{m^{2} (m^{4} n (15 π))}{m^{2} (5 π^{2} (3 n^{4}))}$

Step 4.2.2

Cancel the common factor.

$\frac{m^{2} (m^{4} n (15 π))}{m^{2} (5 π^{2} (3 n^{4}))}$

Step 4.2.3

Rewrite the expression.

$\frac{m^{4} n (15 π)}{5 π^{2} (3 n^{4})}$

Step 5

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

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Step 5.1

Factor $n$ out of $m^{4} n (15 π)$ .

$\frac{n (m^{4} (15 π))}{5 π^{2} (3 n^{4})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $n$ out of $5 π^{2} (3 n^{4})$ .

$\frac{n (m^{4} (15 π))}{n (5 π^{2} (3 n^{3}))}$

Step 5.2.2

Cancel the common factor.

$\frac{n (m^{4} (15 π))}{n (5 π^{2} (3 n^{3}))}$

Step 5.2.3

Rewrite the expression.

$\frac{m^{4} (15 π)}{5 π^{2} (3 n^{3})}$

Step 6

Cancel the common factor of $15$ and $5$ .

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Step 6.1

Factor $5$ out of $m^{4} (15 π)$ .

$\frac{5 (m^{4} (3 π))}{5 π^{2} (3 n^{3})}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $5 π^{2} (3 n^{3})$ .

$\frac{5 (m^{4} (3 π))}{5 (π^{2} (3 n^{3}))}$

Step 6.2.2

Cancel the common factor.

$\frac{5 (m^{4} (3 π))}{5 (π^{2} (3 n^{3}))}$

Step 6.2.3

Rewrite the expression.

$\frac{m^{4} (3 π)}{π^{2} (3 n^{3})}$

Step 7

Cancel the common factor of $3$ .

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Step 7.1

Cancel the common factor.

$\frac{m^{4} (3 π)}{π^{2} (3 n^{3})}$

Step 7.2

Rewrite the expression.

$\frac{m^{4} (π)}{π^{2} (n^{3})}$

Step 8

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

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Step 8.1

Factor $π$ out of $m^{4} (π)$ .

$\frac{π m^{4}}{π^{2} (n^{3})}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $π$ out of $π^{2} (n^{3})$ .

$\frac{π m^{4}}{π (π n^{3})}$

Step 8.2.2

Cancel the common factor.

$\frac{π m^{4}}{π (π n^{3})}$

Step 8.2.3

Rewrite the expression.

$\frac{m^{4}}{π n^{3}}$