Pre-Algebra Examples

$\frac{50 x^{10}}{2 y^{9}} \div \frac{625 x^{8}}{10 y^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{50 x^{10}}{2 y^{9}} \cdot \frac{10 y^{4}}{625 x^{8}}$

Step 2

Combine.

$\frac{50 x^{10} (10 y^{4})}{2 y^{9} (625 x^{8})}$

Step 3

Cancel the common factor of $50$ and $2$ .

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Step 3.1

Factor $2$ out of $50 x^{10} (10 y^{4})$ .

$\frac{2 (25 x^{10} (10 y^{4}))}{2 y^{9} (625 x^{8})}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $2 y^{9} (625 x^{8})$ .

$\frac{2 (25 x^{10} (10 y^{4}))}{2 (y^{9} (625 x^{8}))}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (25 x^{10} (10 y^{4}))}{2 (y^{9} (625 x^{8}))}$

Step 3.2.3

Rewrite the expression.

$\frac{25 x^{10} (10 y^{4})}{y^{9} (625 x^{8})}$

Step 4

Cancel the common factor of $25$ and $625$ .

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Step 4.1

Factor $25$ out of $25 x^{10} (10 y^{4})$ .

$\frac{25 (x^{10} (10 y^{4}))}{y^{9} (625 x^{8})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $25$ out of $y^{9} (625 x^{8})$ .

$\frac{25 (x^{10} (10 y^{4}))}{25 (y^{9} (25 x^{8}))}$

Step 4.2.2

Cancel the common factor.

$\frac{25 (x^{10} (10 y^{4}))}{25 (y^{9} (25 x^{8}))}$

Step 4.2.3

Rewrite the expression.

$\frac{x^{10} (10 y^{4})}{y^{9} (25 x^{8})}$

Step 5

Cancel the common factor of $x^{10}$ and $x^{8}$ .

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Step 5.1

Factor $x^{8}$ out of $x^{10} (10 y^{4})$ .

$\frac{x^{8} (x^{2} (10 y^{4}))}{y^{9} (25 x^{8})}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x^{8}$ out of $y^{9} (25 x^{8})$ .

$\frac{x^{8} (x^{2} (10 y^{4}))}{x^{8} (y^{9} \cdot (25))}$

Step 5.2.2

Cancel the common factor.

$\frac{x^{8} (x^{2} (10 y^{4}))}{x^{8} (y^{9} \cdot (25))}$

Step 5.2.3

Rewrite the expression.

$\frac{x^{2} (10 y^{4})}{y^{9} \cdot (25)}$

Step 6

Cancel the common factor of $10$ and $25$ .

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Step 6.1

Factor $5$ out of $x^{2} (10 y^{4})$ .

$\frac{5 (x^{2} (2 y^{4}))}{y^{9} \cdot (25)}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $5$ out of $y^{9} \cdot (25)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $y^{4}$ and $y^{9}$ .

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Step 7.1

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

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $y^{4}$ out of $y^{9} \cdot (5)$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

Move $2$ to the left of $x^{2}$ .

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

Step 9

Move $5$ to the left of $y^{5}$ .

$\frac{2 x^{2}}{5 y^{5}}$