Algebra Examples

$\frac{2 m n^{2} {(3 m^{2} n)}^{2}}{12 m^{3} n^{4}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $2$ and $12$ .

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Step 1.1.1

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

$\frac{2 (m n^{2} {(3 m^{2} n)}^{2})}{12 m^{3} n^{4}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $2$ out of $12 m^{3} n^{4}$ .

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $m$ out of $6 m^{3} n^{4}$ .

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Cancel the common factors.

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Step 1.3.2.1

Factor $n^{2}$ out of $6 m^{2} n^{4}$ .

$\frac{n^{2} ({(3 m^{2} n)}^{2})}{n^{2} (6 m^{2} n^{2})}$

Step 1.3.2.2

Cancel the common factor.

$\frac{n^{2} {(3 m^{2} n)}^{2}}{n^{2} (6 m^{2} n^{2})}$

Step 1.3.2.3

Rewrite the expression.

$\frac{{(3 m^{2} n)}^{2}}{6 m^{2} n^{2}}$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $3 m^{2} n$ .

$\frac{{(3 m^{2})}^{2} n^{2}}{6 m^{2} n^{2}}$

Step 2.2

Apply the product rule to $3 m^{2}$ .

$\frac{3^{2} {(m^{2})}^{2} n^{2}}{6 m^{2} n^{2}}$

Step 2.3

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

$\frac{9 {(m^{2})}^{2} n^{2}}{6 m^{2} n^{2}}$

Step 2.4

Multiply the exponents in ${(m^{2})}^{2}$ .

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Step 2.4.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{9 m^{2 \cdot 2} n^{2}}{6 m^{2} n^{2}}$

Step 2.4.2

Multiply $2$ by $2$ .

$\frac{9 m^{4} n^{2}}{6 m^{2} n^{2}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

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

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Step 3.1.1

Factor $3$ out of $9 m^{4} n^{2}$ .

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

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $3$ out of $6 m^{2} n^{2}$ .

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

Step 3.1.2.2

Cancel the common factor.

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

Step 3.1.2.3

Rewrite the expression.

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

Step 3.2

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

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Step 3.2.1

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

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

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

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

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

Step 3.2.2.2

Cancel the common factor.

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

Step 3.2.2.3

Rewrite the expression.

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

Step 3.3

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

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

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