Algebra Examples

$\frac{5 x^{6}}{x^{2} y} \div \frac{10 x^{2}}{y}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{5 x^{6}}{x^{2} y} \cdot \frac{y}{10 x^{2}}$

Step 2

Combine.

$\frac{5 x^{6} y}{x^{2} y (10 x^{2})}$

Step 3

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

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Step 3.1

Move $x^{2}$ .

$\frac{5 x^{6} y}{x^{2} x^{2} y \cdot 10}$

Step 3.2

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

$\frac{5 x^{6} y}{x^{2 + 2} y \cdot 10}$

Step 3.3

Add $2$ and $2$ .

$\frac{5 x^{6} y}{x^{4} y \cdot 10}$

Step 4

Cancel the common factor of $5$ and $10$ .

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Step 4.1

Factor $5$ out of $5 x^{6} y$ .

$\frac{5 (x^{6} y)}{x^{4} y \cdot 10}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $5$ out of $x^{4} y \cdot 10$ .

$\frac{5 (x^{6} y)}{5 (x^{4} y \cdot 2)}$

Step 4.2.2

Cancel the common factor.

$\frac{5 (x^{6} y)}{5 (x^{4} y \cdot 2)}$

Step 4.2.3

Rewrite the expression.

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

Step 5

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

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Cancel the common factor of $y$ .

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Step 6.1

Cancel the common factor.

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

Step 6.2

Rewrite the expression.

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