Precalculus Examples

$\frac{12 a^{2} b}{15} \cdot \frac{5 a b}{8 b^{2}}$

Step 1

Combine.

$\frac{12 a^{2} b (5 a b)}{15 (8 b^{2})}$

Step 2

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

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Step 2.1

Move $a$ .

$\frac{12 (a \cdot a^{2}) b (5 b)}{15 (8 b^{2})}$

Step 2.2

Multiply $a$ by $a^{2}$ .

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Step 2.2.1

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

$\frac{12 (a^{1} a^{2}) b (5 b)}{15 (8 b^{2})}$

Step 2.2.2

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

$\frac{12 a^{1 + 2} b (5 b)}{15 (8 b^{2})}$

Step 2.3

Add $1$ and $2$ .

$\frac{12 a^{3} b (5 b)}{15 (8 b^{2})}$

Step 3

Multiply $b$ by $b$ by adding the exponents.

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Step 3.1

Move $b$ .

$\frac{12 a^{3} (b \cdot b) \cdot 5}{15 (8 b^{2})}$

Step 3.2

Multiply $b$ by $b$ .

$\frac{12 a^{3} b^{2} \cdot 5}{15 (8 b^{2})}$

Step 4

Cancel the common factor of $12$ and $15$ .

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Step 4.1

Factor $3$ out of $12 a^{3} b^{2} \cdot 5$ .

$\frac{3 (4 a^{3} b^{2} \cdot 5)}{15 (8 b^{2})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $15 (8 b^{2})$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

Factor $4$ out of $4 a^{3} b^{2} \cdot 5$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $4$ out of $5 (8 b^{2})$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $b^{2}$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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

Step 7

Cancel the common factor of $5$ .

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Step 7.1

Cancel the common factor.

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

Step 7.2

Rewrite the expression.

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