Algebra Examples

$\frac{1}{4} a^{5} b^{12} \times \frac{16}{5} a^{3} b^{2}$

Step 1

Multiply $a^{5}$ by $a^{3}$ by adding the exponents.

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Step 1.1

Move $a^{3}$ .

$\frac{1}{4} \cdot (a^{3} a^{5} b^{12}) \cdot \frac{16}{5} \cdot b^{2}$

Step 1.2

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

$\frac{1}{4} \cdot (a^{3 + 5} b^{12}) \cdot \frac{16}{5} \cdot b^{2}$

Step 1.3

Add $3$ and $5$ .

$\frac{1}{4} \cdot (a^{8} b^{12}) \cdot \frac{16}{5} \cdot b^{2}$

Step 2

Multiply $b^{12}$ by $b^{2}$ by adding the exponents.

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Step 2.1

Move $b^{2}$ .

$\frac{1}{4} \cdot (a^{8} (b^{2} b^{12})) \cdot \frac{16}{5}$

Step 2.2

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

$\frac{1}{4} \cdot (a^{8} b^{2 + 12}) \cdot \frac{16}{5}$

Step 2.3

Add $2$ and $12$ .

$\frac{1}{4} \cdot (a^{8} b^{14}) \cdot \frac{16}{5}$

Step 3

Multiply $\frac{1}{4} (a^{8} b^{14})$ .

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Step 3.1

Combine $a^{8}$ and $\frac{1}{4}$ .

$\frac{a^{8}}{4} b^{14} \cdot \frac{16}{5}$

Step 3.2

Combine $\frac{a^{8}}{4}$ and $b^{14}$ .

$\frac{a^{8} b^{14}}{4} \cdot \frac{16}{5}$

Step 4

Combine.

$\frac{a^{8} b^{14} \cdot 16}{4 \cdot 5}$

Step 5

Cancel the common factor of $16$ and $4$ .

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Step 5.1

Factor $4$ out of $a^{8} b^{14} \cdot 16$ .

$\frac{4 (a^{8} b^{14} \cdot 4)}{4 \cdot 5}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{4 (a^{8} b^{14} \cdot 4)}{4 (5)}$

Step 5.2.2

Cancel the common factor.

$\frac{4 (a^{8} b^{14} \cdot 4)}{4 \cdot 5}$

Step 5.2.3

Rewrite the expression.

$\frac{a^{8} b^{14} \cdot 4}{5}$

Step 6

Move $4$ to the left of $a^{8} b^{14}$ .

$\frac{4 a^{8} b^{14}}{5}$