Algebra Examples

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

Step 1

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

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Step 1.1

Move $y^{3}$ .

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

Step 1.2

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

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

Step 1.3

Add $3$ and $3$ .

$\frac{2 y^{6} \cdot (3 x)}{3 x^{2} y^{4}}$

Step 2

Cancel the common factor of $y^{6}$ and $y^{4}$ .

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Step 2.1

Factor $y^{4}$ out of $2 y^{6} \cdot (3 x)$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

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

Step 4

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

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Step 4.1

Factor $x$ out of $2 y^{2} \cdot (x)$ .

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x$ out of $x^{2}$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

$\frac{2 y^{2}}{x}$