Basic Math Examples

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

Step 1

Combine.

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

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 n m$ .

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

Step 2.2

Apply the product rule to $2 m$ .

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

Step 2.3

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

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Step 2.3.1

Move $m^{3}$ .

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

Step 2.3.2

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

$\frac{{(3 n)}^{2} m^{3 + 2} \cdot 2^{3}}{4 m^{3} n^{4}}$

Step 2.3.3

Add $3$ and $2$ .

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

Step 2.4

Apply the product rule to $3 n$ .

$\frac{3^{2} n^{2} m^{5} \cdot 2^{3}}{4 m^{3} n^{4}}$

Step 2.5

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

$\frac{9 n^{2} m^{5} \cdot 2^{3}}{4 m^{3} n^{4}}$

Step 2.6

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

$\frac{9 n^{2} m^{5} \cdot 8}{4 m^{3} n^{4}}$

Step 2.7

Multiply $8$ by $9$ .

$\frac{72 n^{2} m^{5}}{4 m^{3} n^{4}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $72$ and $4$ .

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Step 3.1.1

Factor $4$ out of $72 n^{2} m^{5}$ .

$\frac{4 (18 n^{2} m^{5})}{4 m^{3} n^{4}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $4$ out of $4 m^{3} n^{4}$ .

$\frac{4 (18 n^{2} m^{5})}{4 (m^{3} n^{4})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{4 (18 n^{2} m^{5})}{4 (m^{3} n^{4})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{18 n^{2} m^{5}}{m^{3} n^{4}}$

Step 3.2

Cancel the common factor of $n^{2}$ and $n^{4}$ .

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Step 3.2.1

Factor $n^{2}$ out of $18 n^{2} m^{5}$ .

$\frac{n^{2} (18 m^{5})}{m^{3} n^{4}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $n^{2}$ out of $m^{3} n^{4}$ .

$\frac{n^{2} (18 m^{5})}{n^{2} (m^{3} n^{2})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{n^{2} (18 m^{5})}{n^{2} (m^{3} n^{2})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{18 m^{5}}{m^{3} n^{2}}$

Step 3.3

Cancel the common factor of $m^{5}$ and $m^{3}$ .

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Step 3.3.1

Factor $m^{3}$ out of $18 m^{5}$ .

$\frac{m^{3} (18 m^{2})}{m^{3} n^{2}}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $m^{3}$ out of $m^{3} n^{2}$ .

$\frac{m^{3} (18 m^{2})}{m^{3} (n^{2})}$

Step 3.3.2.2

Cancel the common factor.

$\frac{m^{3} (18 m^{2})}{m^{3} n^{2}}$

Step 3.3.2.3

Rewrite the expression.

$\frac{18 m^{2}}{n^{2}}$