Basic Math Examples

$(\frac{5}{7} \cdot (m^{3} n^{9})) (\frac{14}{15} \cdot (m^{9} n^{12}))$

Step 1

Multiply $m^{3}$ by $m^{9}$ by adding the exponents.

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Step 1.1

Move $m^{9}$ .

$\frac{5}{7} \cdot (m^{9} m^{3} n^{9}) (\frac{14}{15} \cdot (n^{12}))$

Step 1.2

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

$\frac{5}{7} \cdot (m^{9 + 3} n^{9}) (\frac{14}{15} \cdot (n^{12}))$

Step 1.3

Add $9$ and $3$ .

$\frac{5}{7} \cdot (m^{12} n^{9}) (\frac{14}{15} \cdot (n^{12}))$

Step 2

Multiply $n^{9}$ by $n^{12}$ by adding the exponents.

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Step 2.1

Move $n^{12}$ .

$\frac{5}{7} \cdot (m^{12} (n^{12} n^{9})) \frac{14}{15}$

Step 2.2

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

$\frac{5}{7} \cdot (m^{12} n^{12 + 9}) \frac{14}{15}$

Step 2.3

Add $12$ and $9$ .

$\frac{5}{7} \cdot (m^{12} n^{21}) \frac{14}{15}$

Step 3

Multiply $\frac{5}{7} (m^{12} n^{21})$ .

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Step 3.1

Combine $m^{12}$ and $\frac{5}{7}$ .

$\frac{m^{12} \cdot 5}{7} n^{21} \frac{14}{15}$

Step 3.2

Combine $\frac{m^{12} \cdot 5}{7}$ and $n^{21}$ .

$\frac{m^{12} \cdot 5 n^{21}}{7} \cdot \frac{14}{15}$

Step 4

Combine.

$\frac{m^{12} \cdot 5 n^{21} \cdot 14}{7 \cdot 15}$

Step 5

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

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Step 5.1

Factor $5$ out of $m^{12} \cdot 5 n^{21} \cdot 14$ .

$\frac{5 (m^{12} n^{21} \cdot 14)}{7 \cdot 15}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $5$ out of $7 \cdot 15$ .

$\frac{5 (m^{12} n^{21} \cdot 14)}{5 (7 \cdot 3)}$

Step 5.2.2

Cancel the common factor.

$\frac{5 (m^{12} n^{21} \cdot 14)}{5 (7 \cdot 3)}$

Step 5.2.3

Rewrite the expression.

$\frac{m^{12} n^{21} \cdot 14}{7 \cdot 3}$

Step 6

Cancel the common factor of $14$ and $7$ .

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Step 6.1

Factor $7$ out of $m^{12} n^{21} \cdot 14$ .

$\frac{7 (m^{12} n^{21} \cdot 2)}{7 \cdot 3}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $7$ out of $7 \cdot 3$ .

$\frac{7 (m^{12} n^{21} \cdot 2)}{7 (3)}$

Step 6.2.2

Cancel the common factor.

$\frac{7 (m^{12} n^{21} \cdot 2)}{7 \cdot 3}$

Step 6.2.3

Rewrite the expression.

$\frac{m^{12} n^{21} \cdot 2}{3}$

Step 7

Move $2$ to the left of $m^{12} n^{21}$ .

$\frac{2 m^{12} n^{21}}{3}$