Finite Math Examples

$\frac{4 x^{2} \cdot (2 x^{2})}{12 x \cdot (3 x)}$

Step 1

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

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Step 1.1

Move $x^{2}$ .

$\frac{4 (x^{2} x^{2}) \cdot 2}{12 x \cdot (3 x)}$

Step 1.2

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

$\frac{4 x^{2 + 2} \cdot 2}{12 x \cdot (3 x)}$

Step 1.3

Add $2$ and $2$ .

$\frac{4 x^{4} \cdot 2}{12 x \cdot (3 x)}$

Step 2

Multiply $x$ by $x$ by adding the exponents.

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Step 2.1

Move $x$ .

$\frac{4 x^{4} \cdot 2}{12 (x \cdot x) \cdot 3}$

Step 2.2

Multiply $x$ by $x$ .

$\frac{4 x^{4} \cdot 2}{12 x^{2} \cdot 3}$

Step 3

Cancel the common factor of $4$ and $12$ .

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Step 3.1

Factor $4$ out of $4 x^{4} \cdot 2$ .

$\frac{4 (x^{4} \cdot 2)}{12 x^{2} \cdot 3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $12 x^{2} \cdot 3$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{x^{4} \cdot 2}{3 x^{2} \cdot 3}$

Step 4

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

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Step 4.1

Factor $x^{2}$ out of $x^{4} \cdot 2$ .

$\frac{x^{2} (x^{2} \cdot 2)}{3 x^{2} \cdot 3}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x^{2}$ out of $3 x^{2} \cdot 3$ .

$\frac{x^{2} (x^{2} \cdot 2)}{x^{2} (3 \cdot 3)}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{2} (x^{2} \cdot 2)}{x^{2} (3 \cdot 3)}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{2} \cdot 2}{3 \cdot 3}$

Step 5

Simplify the expression.

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Step 5.1

Multiply $3$ by $3$ .

$\frac{x^{2} \cdot 2}{9}$

Step 5.2

Move $2$ to the left of $x^{2}$ .

$\frac{2 x^{2}}{9}$