Basic Math Examples

$\frac{9 y}{2 b} \div \frac{3 y}{4 b^{3} y^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{9 y}{2 b} \cdot \frac{4 b^{3} y^{4}}{3 y}$

Step 2

Combine.

$\frac{9 y (4 b^{3} y^{4})}{2 b (3 y)}$

Step 3

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

Tap for more steps...

Step 3.1

Move $y^{4}$ .

$\frac{9 (y^{4} y) (4 b^{3})}{2 b (3 y)}$

Step 3.2

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

Tap for more steps...

Step 3.2.1

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

$\frac{9 (y^{4} y^{1}) (4 b^{3})}{2 b (3 y)}$

Step 3.2.2

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

$\frac{9 y^{4 + 1} (4 b^{3})}{2 b (3 y)}$

$\frac{9 y^{4 + 1} (4 b^{3})}{2 b (3 y)}$

Step 3.3

Add $4$ and $1$ .

$\frac{9 y^{5} (4 b^{3})}{2 b (3 y)}$

$\frac{9 y^{5} (4 b^{3})}{2 b (3 y)}$

Step 4

Cancel the common factor of $9$ and $3$ .

Tap for more steps...

Step 4.1

Factor $3$ out of $9 y^{5} (4 b^{3})$ .

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

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $3$ out of $2 b (3 y)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

Cancel the common factor of $y^{5}$ and $y$ .

Tap for more steps...

Step 5.1

Factor $y$ out of $3 y^{5} (4 b^{3})$ .

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

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $y$ out of $2 b (y)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

Tap for more steps...

Step 6.1

Factor $2$ out of $3 y^{4} (4 b^{3})$ .

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

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $2$ out of $2 b$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

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

Tap for more steps...

Step 7.1

Factor $b$ out of $3 y^{4} (2 b^{3})$ .

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

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

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

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

Step 7.2.2

Factor $b$ out of $b^{1}$ .

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

Step 7.2.3

Cancel the common factor.

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

Step 7.2.4

Rewrite the expression.

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

Step 7.2.5

Divide $3 y^{4} (2 b^{2})$ by $1$ .

$3 y^{4} (2 b^{2})$

$3 y^{4} (2 b^{2})$

$3 y^{4} (2 b^{2})$

Step 8

Simplify the expression.

Tap for more steps...

Step 8.1

Rewrite using the commutative property of multiplication.

$3 \cdot 2 y^{4} b^{2}$

Step 8.2

Multiply $3$ by $2$ .

$6 y^{4} b^{2}$

$6 y^{4} b^{2}$

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