Precalculus Examples

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

Step 1

Combine.

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

Step 2

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

Tap for more steps...

Step 2.1

Move $b^{2}$ .

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

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

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

Tap for more steps...

Step 3.1

Move $a^{2}$ .

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

Step 3.2

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

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

Step 3.3

Add $2$ and $2$ .

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

Step 4

Multiply $b^{3}$ by $b^{4}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $b^{4}$ .

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

Step 4.2

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

$\frac{4 a^{3} b^{3} \cdot 3}{a^{4} b^{4 + 3} \cdot 2}$

Step 4.3

Add $4$ and $3$ .

$\frac{4 a^{3} b^{3} \cdot 3}{a^{4} b^{7} \cdot 2}$

Step 5

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

Tap for more steps...

Step 5.1

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

$\frac{2 (2 a^{3} b^{3} \cdot 3)}{a^{4} b^{7} \cdot 2}$

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $2$ out of $a^{4} b^{7} \cdot 2$ .

$\frac{2 (2 a^{3} b^{3} \cdot 3)}{2 \cdot (a^{4} b^{7})}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (2 a^{3} b^{3} \cdot 3)}{2 \cdot (a^{4} b^{7})}$

Step 5.2.3

Rewrite the expression.

$\frac{2 a^{3} b^{3} \cdot 3}{a^{4} b^{7}}$

Step 6

Cancel the common factor of $a^{3}$ and $a^{4}$ .

Tap for more steps...

Step 6.1

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

$\frac{a^{3} (2 b^{3} \cdot 3)}{a^{4} b^{7}}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $a^{3}$ out of $a^{4} b^{7}$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $b^{3}$ and $b^{7}$ .

Tap for more steps...

Step 7.1

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

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

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $b^{3}$ out of $a b^{7}$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Multiply $2$ by $3$ .

$\frac{6}{a b^{4}}$