Pre-Algebra Examples

$\frac{81 x^{9}}{y^{4}} \cdot \frac{x^{2}}{36 x^{5} y}$

Step 1

Combine.

$\frac{81 x^{9} x^{2}}{y^{4} (36 x^{5} y)}$

Step 2

Multiply $x^{9}$ by $x^{2}$ by adding the exponents.

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Step 2.1

Move $x^{2}$ .

$\frac{81 (x^{2} x^{9})}{y^{4} (36 x^{5} y)}$

Step 2.2

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

$\frac{81 x^{2 + 9}}{y^{4} (36 x^{5} y)}$

Step 2.3

Add $2$ and $9$ .

$\frac{81 x^{11}}{y^{4} (36 x^{5} y)}$

Step 3

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

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Step 3.1

Move $y$ .

$\frac{81 x^{11}}{y \cdot y^{4} (36 x^{5})}$

Step 3.2

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

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Step 3.2.1

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

$\frac{81 x^{11}}{y^{1} y^{4} (36 x^{5})}$

Step 3.2.2

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

$\frac{81 x^{11}}{y^{1 + 4} (36 x^{5})}$

Step 3.3

Add $1$ and $4$ .

$\frac{81 x^{11}}{y^{5} (36 x^{5})}$

Step 4

Cancel the common factor of $81$ and $36$ .

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Step 4.1

Factor $9$ out of $81 x^{11}$ .

$\frac{9 (9 x^{11})}{y^{5} (36 x^{5})}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $9$ out of $y^{5} (36 x^{5})$ .

$\frac{9 (9 x^{11})}{9 (y^{5} (4 x^{5}))}$

Step 4.2.2

Cancel the common factor.

$\frac{9 (9 x^{11})}{9 (y^{5} (4 x^{5}))}$

Step 4.2.3

Rewrite the expression.

$\frac{9 x^{11}}{y^{5} (4 x^{5})}$

Step 5

Cancel the common factor of $x^{11}$ and $x^{5}$ .

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Step 5.1

Factor $x^{5}$ out of $9 x^{11}$ .

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

Move $4$ to the left of $y^{5}$ .

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