Algebra Examples

$\frac{8}{2 a^{5}} \cdot \frac{6}{12 a^{2}}$

Step 1

Combine.

$\frac{8 \cdot 6}{2 a^{5} (12 a^{2})}$

Step 2

Multiply $a^{5}$ by $a^{2}$ by adding the exponents.

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Step 2.1

Move $a^{2}$ .

$\frac{8 \cdot 6}{2 (a^{2} a^{5}) \cdot 12}$

Step 2.2

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

$\frac{8 \cdot 6}{2 a^{2 + 5} \cdot 12}$

Step 2.3

Add $2$ and $5$ .

$\frac{8 \cdot 6}{2 a^{7} \cdot 12}$

$\frac{8 \cdot 6}{2 a^{7} \cdot 12}$

Step 3

Cancel the common factor of $8$ and $2$ .

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Step 3.1

Factor $2$ out of $8 \cdot 6$ .

$\frac{2 (4 \cdot 6)}{2 a^{7} \cdot 12}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 a^{7} \cdot 12$ .

$\frac{2 (4 \cdot 6)}{2 (a^{7} \cdot 12)}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (4 \cdot 6)}{2 (a^{7} \cdot 12)}$

Step 3.2.3

Rewrite the expression.

$\frac{4 \cdot 6}{a^{7} \cdot 12}$

$\frac{4 \cdot 6}{a^{7} \cdot 12}$

$\frac{4 \cdot 6}{a^{7} \cdot 12}$

Step 4

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

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Step 4.1

Factor $4$ out of $4 \cdot 6$ .

$\frac{4 (6)}{a^{7} \cdot 12}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $a^{7} \cdot 12$ .

$\frac{4 (6)}{4 (a^{7} \cdot 3)}$

Step 4.2.2

Cancel the common factor.

$\frac{4 \cdot 6}{4 (a^{7} \cdot 3)}$

Step 4.2.3

Rewrite the expression.

$\frac{6}{a^{7} \cdot 3}$

$\frac{6}{a^{7} \cdot 3}$

$\frac{6}{a^{7} \cdot 3}$

Step 5

Cancel the common factor of $6$ and $3$ .

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Step 5.1

Factor $3$ out of $6$ .

$\frac{3 \cdot 2}{a^{7} \cdot 3}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $a^{7} \cdot 3$ .

$\frac{3 \cdot 2}{3 \cdot a^{7}}$

Step 5.2.2

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot a^{7}}$

Step 5.2.3

Rewrite the expression.

$\frac{2}{a^{7}}$

$\frac{2}{a^{7}}$

$\frac{2}{a^{7}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$