Algebra Examples

$\frac{5 a^{3}}{a b} \cdot \frac{2 a}{35}$

Step 1

Combine.

$\frac{5 a^{3} (2 a)}{a b \cdot 35}$

Step 2

Multiply $a^{3}$ by $a$ by adding the exponents.

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Step 2.1

Move $a$ .

$\frac{5 (a \cdot a^{3}) \cdot 2}{a b \cdot 35}$

Step 2.2

Multiply $a$ by $a^{3}$ .

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Step 2.2.1

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

$\frac{5 (a^{1} a^{3}) \cdot 2}{a b \cdot 35}$

Step 2.2.2

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

$\frac{5 a^{1 + 3} \cdot 2}{a b \cdot 35}$

$\frac{5 a^{1 + 3} \cdot 2}{a b \cdot 35}$

Step 2.3

Add $1$ and $3$ .

$\frac{5 a^{4} \cdot 2}{a b \cdot 35}$

$\frac{5 a^{4} \cdot 2}{a b \cdot 35}$

Step 3

Cancel the common factor of $5$ and $35$ .

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Step 3.1

Factor $5$ out of $5 a^{4} \cdot 2$ .

$\frac{5 (a^{4} \cdot 2)}{a b \cdot 35}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $5$ out of $a b \cdot 35$ .

$\frac{5 (a^{4} \cdot 2)}{5 (a b \cdot 7)}$

Step 3.2.2

Cancel the common factor.

$\frac{5 (a^{4} \cdot 2)}{5 (a b \cdot 7)}$

Step 3.2.3

Rewrite the expression.

$\frac{a^{4} \cdot 2}{a b \cdot 7}$

$\frac{a^{4} \cdot 2}{a b \cdot 7}$

$\frac{a^{4} \cdot 2}{a b \cdot 7}$

Step 4

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

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Step 4.1

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

$\frac{a (a^{3} \cdot 2)}{a b \cdot 7}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $a$ out of $a b \cdot 7$ .

$\frac{a (a^{3} \cdot 2)}{a (b \cdot 7)}$

Step 4.2.2

Cancel the common factor.

$\frac{a (a^{3} \cdot 2)}{a (b \cdot 7)}$

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Reorder.

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Step 5.1

Move $2$ to the left of $a^{3}$ .

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

Step 5.2

Move $7$ to the left of $b$ .

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

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

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