Algebra Examples

$\frac{4 a \cdot 6 a^{5}}{8 a^{2}}$

Step 1

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

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Step 1.1

Move $a^{5}$ .

$\frac{4 (a^{5} a) \cdot 6}{8 a^{2}}$

Step 1.2

Multiply $a^{5}$ by $a$ .

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Step 1.2.1

Raise $a$ to the power of $1$ .

$\frac{4 (a^{5} a^{1}) \cdot 6}{8 a^{2}}$

Step 1.2.2

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

$\frac{4 a^{5 + 1} \cdot 6}{8 a^{2}}$

$\frac{4 a^{5 + 1} \cdot 6}{8 a^{2}}$

Step 1.3

Add $5$ and $1$ .

$\frac{4 a^{6} \cdot 6}{8 a^{2}}$

$\frac{4 a^{6} \cdot 6}{8 a^{2}}$

Step 2

Cancel the common factor of $4$ and $8$ .

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Step 2.1

Factor $4$ out of $4 a^{6} \cdot 6$ .

$\frac{4 (a^{6} \cdot 6)}{8 a^{2}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $8 a^{2}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

$\frac{a^{6} \cdot 6}{2 a^{2}}$

$\frac{a^{6} \cdot 6}{2 a^{2}}$

$\frac{a^{6} \cdot 6}{2 a^{2}}$

Step 3

Cancel the common factor of $a^{6}$ and $a^{2}$ .

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Step 3.1

Factor $a^{2}$ out of $a^{6} \cdot 6$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $a^{2}$ out of $2 a^{2}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{a^{4} \cdot 6}{2}$

$\frac{a^{4} \cdot 6}{2}$

$\frac{a^{4} \cdot 6}{2}$

Step 4

Cancel the common factor of $6$ and $2$ .

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Step 4.1

Factor $2$ out of $a^{4} \cdot 6$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $2$ out of $2$ .

$\frac{2 (a^{4} \cdot 3)}{2 (1)}$

Step 4.2.2

Cancel the common factor.

$\frac{2 (a^{4} \cdot 3)}{2 \cdot 1}$

Step 4.2.3

Rewrite the expression.

$\frac{a^{4} \cdot 3}{1}$

Step 4.2.4

Divide $a^{4} \cdot 3$ by $1$ .

$a^{4} \cdot 3$

$a^{4} \cdot 3$

$a^{4} \cdot 3$

Step 5

Move $3$ to the left of $a^{4}$ .

$3 a^{4}$

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