Basic Math Examples

$\frac{9 b^{2} y^{5}}{2 y} \cdot \frac{8 y}{3 b}$

Step 1

Combine.

$\frac{9 b^{2} y^{5} (8 y)}{2 y (3 b)}$

Step 2

Multiply $y^{5}$ by $y$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $y$ .

$\frac{9 b^{2} (y \cdot y^{5}) \cdot 8}{2 y (3 b)}$

Step 2.2

Multiply $y$ by $y^{5}$ .

Tap for more steps...

Step 2.2.1

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

$\frac{9 b^{2} (y^{1} y^{5}) \cdot 8}{2 y (3 b)}$

Step 2.2.2

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

$\frac{9 b^{2} y^{1 + 5} \cdot 8}{2 y (3 b)}$

$\frac{9 b^{2} y^{1 + 5} \cdot 8}{2 y (3 b)}$

Step 2.3

Add $1$ and $5$ .

$\frac{9 b^{2} y^{6} \cdot 8}{2 y (3 b)}$

$\frac{9 b^{2} y^{6} \cdot 8}{2 y (3 b)}$

Step 3

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

Tap for more steps...

Step 3.1

Factor $3$ out of $9 b^{2} y^{6} \cdot 8$ .

$\frac{3 (3 b^{2} y^{6} \cdot 8)}{2 y (3 b)}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

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

$\frac{3 (3 b^{2} y^{6} \cdot 8)}{3 (2 y (b))}$

Step 3.2.2

Cancel the common factor.

$\frac{3 (3 b^{2} y^{6} \cdot 8)}{3 (2 y (b))}$

Step 3.2.3

Rewrite the expression.

$\frac{3 b^{2} y^{6} \cdot 8}{2 y (b)}$

$\frac{3 b^{2} y^{6} \cdot 8}{2 y (b)}$

$\frac{3 b^{2} y^{6} \cdot 8}{2 y (b)}$

Step 4

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

Tap for more steps...

Step 4.1

Factor $b$ out of $3 b^{2} y^{6} \cdot 8$ .

$\frac{b (3 b y^{6} \cdot 8)}{2 y (b)}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

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

$\frac{b (3 b y^{6} \cdot 8)}{b (2 y)}$

Step 4.2.2

Cancel the common factor.

$\frac{b (3 b y^{6} \cdot 8)}{b (2 y)}$

Step 4.2.3

Rewrite the expression.

$\frac{3 b y^{6} \cdot 8}{2 y}$

$\frac{3 b y^{6} \cdot 8}{2 y}$

$\frac{3 b y^{6} \cdot 8}{2 y}$

Step 5

Cancel the common factor of $y^{6}$ and $y$ .

Tap for more steps...

Step 5.1

Factor $y$ out of $3 b y^{6} \cdot 8$ .

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

Step 5.2

Cancel the common factors.

Tap for more steps...

Step 5.2.1

Factor $y$ out of $2 y$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

$\frac{3 b y^{5} \cdot 8}{2}$

$\frac{3 b y^{5} \cdot 8}{2}$

$\frac{3 b y^{5} \cdot 8}{2}$

Step 6

Cancel the common factor of $8$ and $2$ .

Tap for more steps...

Step 6.1

Factor $2$ out of $3 b y^{5} \cdot 8$ .

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

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $2$ out of $2$ .

$\frac{2 (3 b y^{5} \cdot 4)}{2 (1)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 (3 b y^{5} \cdot 4)}{2 \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{3 b y^{5} \cdot 4}{1}$

Step 6.2.4

Divide $3 b y^{5} \cdot 4$ by $1$ .

$3 b y^{5} \cdot 4$

$3 b y^{5} \cdot 4$

$3 b y^{5} \cdot 4$

Step 7

Multiply $4$ by $3$ .

$12 b y^{5}$

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