Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{2}$ .

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

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

$\frac{2 x^{2 + 1} y (3 y^{3})}{x^{3} y}$

$\frac{2 x^{2 + 1} y (3 y^{3})}{x^{3} y}$

Step 1.3

Add $2$ and $1$ .

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

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

Step 2

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

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

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

Step 2.3

Add $3$ and $1$ .

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

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

Step 3

Cancel the common factor of $x^{3}$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

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

Step 4

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

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

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

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

Step 4.2.2

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

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

Step 4.2.3

Cancel the common factor.

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

Step 4.2.4

Rewrite the expression.

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

Step 4.2.5

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

$2 y^{3} \cdot 3$

$2 y^{3} \cdot 3$

$2 y^{3} \cdot 3$

Step 5

Multiply $3$ by $2$ .

$6 y^{3}$

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