Basic Math Examples

$8 y \cdot (3 y^{3}) \div 12 y^{2}$

Step 1

Rewrite the division as a fraction.

$\frac{8 y \cdot (3 y^{3})}{12 y^{2}}$

Step 2

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

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Step 2.1

Move $y^{3}$ .

$\frac{8 (y^{3} y) \cdot 3}{12 y^{2}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{8 (y^{3} y^{1}) \cdot 3}{12 y^{2}}$

Step 2.2.2

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

$\frac{8 y^{3 + 1} \cdot 3}{12 y^{2}}$

$\frac{8 y^{3 + 1} \cdot 3}{12 y^{2}}$

Step 2.3

Add $3$ and $1$ .

$\frac{8 y^{4} \cdot 3}{12 y^{2}}$

$\frac{8 y^{4} \cdot 3}{12 y^{2}}$

Step 3

Cancel the common factor of $8$ and $12$ .

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Step 3.1

Factor $4$ out of $8 y^{4} \cdot 3$ .

$\frac{4 (2 y^{4} \cdot 3)}{12 y^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $4$ out of $12 y^{2}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

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

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

Step 4

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $y^{2}$ out of $3 y^{2}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{2 y^{2} \cdot 3}{3}$

$\frac{2 y^{2} \cdot 3}{3}$

$\frac{2 y^{2} \cdot 3}{3}$

Step 5

Cancel the common factor of $3$ .

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Step 5.1

Cancel the common factor.

$\frac{2 y^{2} \cdot 3}{3}$

Step 5.2

Divide $2 y^{2}$ by $1$ .

$2 y^{2}$

$2 y^{2}$

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