Algebra Examples

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

Step 1

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

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Step 1.1

Move $x^{4}$ .

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

Step 1.2

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

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

Step 1.3

Add $4$ and $2$ .

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

Step 2

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

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Step 2.1

Move $y^{3}$ .

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

Step 2.2

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

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Step 2.2.1

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

$\frac{2 x^{6} (y^{3} y^{1}) \cdot 4}{6 x^{6} y^{6}}$

Step 2.2.2

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

$\frac{2 x^{6} y^{3 + 1} \cdot 4}{6 x^{6} y^{6}}$

Step 2.3

Add $3$ and $1$ .

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

Step 3

Cancel the common factor of $2$ and $6$ .

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6 x^{6} y^{6}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

Cancel the common factor of $x^{6}$ .

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Step 4.1

Cancel the common factor.

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

Step 4.2

Rewrite the expression.

$\frac{y^{4} \cdot 4}{3 y^{6}}$

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{4}$ out of $3 y^{6}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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