Algebra Examples

$\frac{2}{5} a^{6} b c^{3} \times \frac{3}{4} a^{11} b^{4} c^{8}$

Step 1

Multiply $a^{6}$ by $a^{11}$ by adding the exponents.

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Step 1.1

Move $a^{11}$ .

$\frac{2}{5} \cdot (a^{11} a^{6} b c^{3}) \cdot \frac{3}{4} \cdot (b^{4} c^{8})$

Step 1.2

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

$\frac{2}{5} \cdot (a^{11 + 6} b c^{3}) \cdot \frac{3}{4} \cdot (b^{4} c^{8})$

Step 1.3

Add $11$ and $6$ .

$\frac{2}{5} \cdot (a^{17} b c^{3}) \cdot \frac{3}{4} \cdot (b^{4} c^{8})$

Step 2

Multiply $b$ by $b^{4}$ by adding the exponents.

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Step 2.1

Move $b^{4}$ .

$\frac{2}{5} \cdot (a^{17} (b^{4} b) c^{3}) \cdot \frac{3}{4} \cdot c^{8}$

Step 2.2

Multiply $b^{4}$ by $b$ .

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Step 2.2.1

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

$\frac{2}{5} \cdot (a^{17} (b^{4} b^{1}) c^{3}) \cdot \frac{3}{4} \cdot c^{8}$

Step 2.2.2

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

$\frac{2}{5} \cdot (a^{17} b^{4 + 1} c^{3}) \cdot \frac{3}{4} \cdot c^{8}$

Step 2.3

Add $4$ and $1$ .

$\frac{2}{5} \cdot (a^{17} b^{5} c^{3}) \cdot \frac{3}{4} \cdot c^{8}$

Step 3

Multiply $c^{3}$ by $c^{8}$ by adding the exponents.

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Step 3.1

Move $c^{8}$ .

$\frac{2}{5} \cdot (a^{17} b^{5} (c^{8} c^{3})) \cdot \frac{3}{4}$

Step 3.2

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

$\frac{2}{5} \cdot (a^{17} b^{5} c^{8 + 3}) \cdot \frac{3}{4}$

Step 3.3

Add $8$ and $3$ .

$\frac{2}{5} \cdot (a^{17} b^{5} c^{11}) \cdot \frac{3}{4}$

Step 4

Multiply $\frac{2}{5} (a^{17} b^{5} c^{11})$ .

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Step 4.1

Combine $a^{17}$ and $\frac{2}{5}$ .

$\frac{a^{17} \cdot 2}{5} (b^{5} c^{11}) \cdot \frac{3}{4}$

Step 4.2

Combine $b^{5}$ and $\frac{a^{17} \cdot 2}{5}$ .

$\frac{b^{5} (a^{17} \cdot 2)}{5} c^{11} \cdot \frac{3}{4}$

Step 4.3

Combine $\frac{b^{5} (a^{17} \cdot 2)}{5}$ and $c^{11}$ .

$\frac{b^{5} (a^{17} \cdot 2) c^{11}}{5} \cdot \frac{3}{4}$

Step 5

Combine.

$\frac{b^{5} (a^{17} \cdot 2) c^{11} \cdot 3}{5 \cdot 4}$

Step 6

Cancel the common factor of $2$ and $4$ .

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Step 6.1

Factor $2$ out of $b^{5} (a^{17} \cdot 2) c^{11} \cdot 3$ .

$\frac{2 (b^{5} (a^{17}) c^{11} \cdot 3)}{5 \cdot 4}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $5 \cdot 4$ .

$\frac{2 (b^{5} (a^{17}) c^{11} \cdot 3)}{2 (5 \cdot 2)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (b^{5} (a^{17}) c^{11} \cdot 3)}{2 (5 \cdot 2)}$

Step 6.2.3

Rewrite the expression.

$\frac{b^{5} (a^{17}) c^{11} \cdot 3}{5 \cdot 2}$

Step 7

Simplify the expression.

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Step 7.1

Multiply $5$ by $2$ .

$\frac{b^{5} a^{17} c^{11} \cdot 3}{10}$

Step 7.2

Move $3$ to the left of $b^{5} a^{17} c^{11}$ .

$\frac{3 b^{5} a^{17} c^{11}}{10}$