Basic Math Examples

$\frac{\frac{8 b}{a^{3}}}{\frac{32}{a b^{3}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{8 b}{a^{3}} \cdot \frac{a b^{3}}{32}$

Step 2

Combine.

$\frac{8 b (a b^{3})}{a^{3} \cdot 32}$

Step 3

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

Tap for more steps...

Step 3.1

Move $b^{3}$ .

$\frac{8 (b^{3} b) a}{a^{3} \cdot 32}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$\frac{8 (b^{3} b^{1}) a}{a^{3} \cdot 32}$

Step 3.2.2

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

$\frac{8 b^{3 + 1} a}{a^{3} \cdot 32}$

$\frac{8 b^{3 + 1} a}{a^{3} \cdot 32}$

Step 3.3

Add $3$ and $1$ .

$\frac{8 b^{4} a}{a^{3} \cdot 32}$

$\frac{8 b^{4} a}{a^{3} \cdot 32}$

Step 4

Cancel the common factor of $8$ and $32$ .

Tap for more steps...

Step 4.1

Factor $8$ out of $8 b^{4} a$ .

$\frac{8 (b^{4} a)}{a^{3} \cdot 32}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $8$ out of $a^{3} \cdot 32$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

Tap for more steps...

Step 5.1

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

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

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

Move $4$ to the left of $a^{2}$ .

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

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