Basic Math Examples

$\frac{9 a^{5} y^{2}}{2 y} \div \frac{3 a}{4 y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{9 a^{5} y^{2}}{2 y} \cdot \frac{4 y}{3 a}$

Step 2

Combine.

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

Step 3

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

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Step 3.1

Move $y$ .

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

Step 3.2

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

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Step 3.2.1

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

$\frac{9 a^{5} (y^{1} y^{2}) \cdot 4}{2 y (3 a)}$

Step 3.2.2

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

$\frac{9 a^{5} y^{1 + 2} \cdot 4}{2 y (3 a)}$

$\frac{9 a^{5} y^{1 + 2} \cdot 4}{2 y (3 a)}$

Step 3.3

Add $1$ and $2$ .

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

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

Step 4

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

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Step 4.1

Factor $3$ out of $9 a^{5} y^{3} \cdot 4$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

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

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

Step 5

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

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Step 5.1

Factor $a$ out of $3 a^{5} y^{3} \cdot 4$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

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

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

Step 6

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

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Step 6.1

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

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y$ out of $2 y$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

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

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

Step 7

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

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $2$ out of $2$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{3 a^{4} y^{2} \cdot 2}{1}$

Step 7.2.4

Divide $3 a^{4} y^{2} \cdot 2$ by $1$ .

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

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

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

Step 8

Multiply $2$ by $3$ .

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

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