Pre-Algebra Examples

$\frac{15 x^{4} y^{5}}{18 x^{6} y} \div \frac{25 x^{12} y^{4}}{12 x^{5} y^{4}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{15 x^{4} y^{5}}{18 x^{6} y} \cdot \frac{12 x^{5} y^{4}}{25 x^{12} y^{4}}$

Step 2

Combine.

$\frac{15 x^{4} y^{5} (12 x^{5} y^{4})}{18 x^{6} y (25 x^{12} y^{4})}$

Step 3

Multiply $x^{4}$ by $x^{5}$ by adding the exponents.

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Step 3.1

Move $x^{5}$ .

$\frac{15 (x^{5} x^{4}) y^{5} (12 y^{4})}{18 x^{6} y (25 x^{12} y^{4})}$

Step 3.2

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

$\frac{15 x^{5 + 4} y^{5} (12 y^{4})}{18 x^{6} y (25 x^{12} y^{4})}$

Step 3.3

Add $5$ and $4$ .

$\frac{15 x^{9} y^{5} (12 y^{4})}{18 x^{6} y (25 x^{12} y^{4})}$

Step 4

Multiply $y^{5}$ by $y^{4}$ by adding the exponents.

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Step 4.1

Move $y^{4}$ .

$\frac{15 x^{9} (y^{4} y^{5}) \cdot 12}{18 x^{6} y (25 x^{12} y^{4})}$

Step 4.2

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

$\frac{15 x^{9} y^{4 + 5} \cdot 12}{18 x^{6} y (25 x^{12} y^{4})}$

Step 4.3

Add $4$ and $5$ .

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{6} y (25 x^{12} y^{4})}$

Step 5

Multiply $x^{6}$ by $x^{12}$ by adding the exponents.

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Step 5.1

Move $x^{12}$ .

$\frac{15 x^{9} y^{9} \cdot 12}{18 (x^{12} x^{6}) y (25 y^{4})}$

Step 5.2

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

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{12 + 6} y (25 y^{4})}$

Step 5.3

Add $12$ and $6$ .

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{18} y (25 y^{4})}$

Step 6

Multiply $y$ by $y^{4}$ by adding the exponents.

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Step 6.1

Move $y^{4}$ .

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{18} (y^{4} y) \cdot 25}$

Step 6.2

Multiply $y^{4}$ by $y$ .

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Step 6.2.1

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

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{18} (y^{4} y^{1}) \cdot 25}$

Step 6.2.2

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

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{18} y^{4 + 1} \cdot 25}$

Step 6.3

Add $4$ and $1$ .

$\frac{15 x^{9} y^{9} \cdot 12}{18 x^{18} y^{5} \cdot 25}$

Step 7

Cancel the common factor of $15$ and $18$ .

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Step 7.1

Factor $3$ out of $15 x^{9} y^{9} \cdot 12$ .

$\frac{3 (5 x^{9} y^{9} \cdot 12)}{18 x^{18} y^{5} \cdot 25}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $3$ out of $18 x^{18} y^{5} \cdot 25$ .

$\frac{3 (5 x^{9} y^{9} \cdot 12)}{3 (6 x^{18} y^{5} \cdot 25)}$

Step 7.2.2

Cancel the common factor.

$\frac{3 (5 x^{9} y^{9} \cdot 12)}{3 (6 x^{18} y^{5} \cdot 25)}$

Step 7.2.3

Rewrite the expression.

$\frac{5 x^{9} y^{9} \cdot 12}{6 x^{18} y^{5} \cdot 25}$

Step 8

Cancel the common factor of $5$ and $25$ .

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Step 8.1

Factor $5$ out of $5 x^{9} y^{9} \cdot 12$ .

$\frac{5 (x^{9} y^{9} \cdot 12)}{6 x^{18} y^{5} \cdot 25}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $5$ out of $6 x^{18} y^{5} \cdot 25$ .

$\frac{5 (x^{9} y^{9} \cdot 12)}{5 (6 x^{18} y^{5} \cdot 5)}$

Step 8.2.2

Cancel the common factor.

$\frac{5 (x^{9} y^{9} \cdot 12)}{5 (6 x^{18} y^{5} \cdot 5)}$

Step 8.2.3

Rewrite the expression.

$\frac{x^{9} y^{9} \cdot 12}{6 x^{18} y^{5} \cdot 5}$

Step 9

Cancel the common factor of $x^{9}$ and $x^{18}$ .

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Step 9.1

Factor $x^{9}$ out of $x^{9} y^{9} \cdot 12$ .

$\frac{x^{9} (y^{9} \cdot 12)}{6 x^{18} y^{5} \cdot 5}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $x^{9}$ out of $6 x^{18} y^{5} \cdot 5$ .

$\frac{x^{9} (y^{9} \cdot 12)}{x^{9} (6 x^{9} y^{5} \cdot 5)}$

Step 9.2.2

Cancel the common factor.

$\frac{x^{9} (y^{9} \cdot 12)}{x^{9} (6 x^{9} y^{5} \cdot 5)}$

Step 9.2.3

Rewrite the expression.

$\frac{y^{9} \cdot 12}{6 x^{9} y^{5} \cdot 5}$

Step 10

Cancel the common factor of $y^{9}$ and $y^{5}$ .

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Step 10.1

Factor $y^{5}$ out of $y^{9} \cdot 12$ .

$\frac{y^{5} (y^{4} \cdot 12)}{6 x^{9} y^{5} \cdot 5}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $y^{5}$ out of $6 x^{9} y^{5} \cdot 5$ .

$\frac{y^{5} (y^{4} \cdot 12)}{y^{5} (6 x^{9} \cdot 5)}$

Step 10.2.2

Cancel the common factor.

$\frac{y^{5} (y^{4} \cdot 12)}{y^{5} (6 x^{9} \cdot 5)}$

Step 10.2.3

Rewrite the expression.

$\frac{y^{4} \cdot 12}{6 x^{9} \cdot 5}$

Step 11

Cancel the common factor of $12$ and $6$ .

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Step 11.1

Factor $6$ out of $y^{4} \cdot 12$ .

$\frac{6 (y^{4} \cdot 2)}{6 x^{9} \cdot 5}$

Step 11.2

Cancel the common factors.

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Step 11.2.1

Factor $6$ out of $6 x^{9} \cdot 5$ .

$\frac{6 (y^{4} \cdot 2)}{6 (x^{9} \cdot 5)}$

Step 11.2.2

Cancel the common factor.

$\frac{6 (y^{4} \cdot 2)}{6 (x^{9} \cdot 5)}$

Step 11.2.3

Rewrite the expression.

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

Step 12

Move $2$ to the left of $y^{4}$ .

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

Step 13

Move $5$ to the left of $x^{9}$ .

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