Algebra Examples

$\frac{6 x^{2} y^{3}}{2 x^{2} y^{2}} \cdot \frac{10 x^{3} y^{4}}{18 y^{2}}$

Step 1

Combine.

$\frac{6 x^{2} y^{3} (10 x^{3} y^{4})}{2 x^{2} y^{2} (18 y^{2})}$

Step 2

Multiply $x^{2}$ by $x^{3}$ by adding the exponents.

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Step 2.1

Move $x^{3}$ .

$\frac{6 (x^{3} x^{2}) y^{3} (10 y^{4})}{2 x^{2} y^{2} (18 y^{2})}$

Step 2.2

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

$\frac{6 x^{3 + 2} y^{3} (10 y^{4})}{2 x^{2} y^{2} (18 y^{2})}$

Step 2.3

Add $3$ and $2$ .

$\frac{6 x^{5} y^{3} (10 y^{4})}{2 x^{2} y^{2} (18 y^{2})}$

Step 3

Multiply $y^{3}$ by $y^{4}$ by adding the exponents.

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Step 3.1

Move $y^{4}$ .

$\frac{6 x^{5} (y^{4} y^{3}) \cdot 10}{2 x^{2} y^{2} (18 y^{2})}$

Step 3.2

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

$\frac{6 x^{5} y^{4 + 3} \cdot 10}{2 x^{2} y^{2} (18 y^{2})}$

Step 3.3

Add $4$ and $3$ .

$\frac{6 x^{5} y^{7} \cdot 10}{2 x^{2} y^{2} (18 y^{2})}$

Step 4

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

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Step 4.1

Move $y^{2}$ .

$\frac{6 x^{5} y^{7} \cdot 10}{2 x^{2} (y^{2} y^{2}) \cdot 18}$

Step 4.2

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

$\frac{6 x^{5} y^{7} \cdot 10}{2 x^{2} y^{2 + 2} \cdot 18}$

Step 4.3

Add $2$ and $2$ .

$\frac{6 x^{5} y^{7} \cdot 10}{2 x^{2} y^{4} \cdot 18}$

Step 5

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

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Step 5.1

Factor $2$ out of $6 x^{5} y^{7} \cdot 10$ .

$\frac{2 (3 x^{5} y^{7} \cdot 10)}{2 x^{2} y^{4} \cdot 18}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $2$ out of $2 x^{2} y^{4} \cdot 18$ .

$\frac{2 (3 x^{5} y^{7} \cdot 10)}{2 (x^{2} y^{4} \cdot 18)}$

Step 5.2.2

Cancel the common factor.

$\frac{2 (3 x^{5} y^{7} \cdot 10)}{2 (x^{2} y^{4} \cdot 18)}$

Step 5.2.3

Rewrite the expression.

$\frac{3 x^{5} y^{7} \cdot 10}{x^{2} y^{4} \cdot 18}$

Step 6

Cancel the common factor of $3$ and $18$ .

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Step 6.1

Factor $3$ out of $3 x^{5} y^{7} \cdot 10$ .

$\frac{3 (x^{5} y^{7} \cdot 10)}{x^{2} y^{4} \cdot 18}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $3$ out of $x^{2} y^{4} \cdot 18$ .

$\frac{3 (x^{5} y^{7} \cdot 10)}{3 (x^{2} y^{4} \cdot 6)}$

Step 6.2.2

Cancel the common factor.

$\frac{3 (x^{5} y^{7} \cdot 10)}{3 (x^{2} y^{4} \cdot 6)}$

Step 6.2.3

Rewrite the expression.

$\frac{x^{5} y^{7} \cdot 10}{x^{2} y^{4} \cdot 6}$

Step 7

Cancel the common factor of $x^{5}$ and $x^{2}$ .

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Step 7.1

Factor $x^{2}$ out of $x^{5} y^{7} \cdot 10$ .

$\frac{x^{2} (x^{3} y^{7} \cdot 10)}{x^{2} y^{4} \cdot 6}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{x^{2} (x^{3} y^{7} \cdot 10)}{x^{2} (y^{4} \cdot 6)}$

Step 7.2.2

Cancel the common factor.

$\frac{x^{2} (x^{3} y^{7} \cdot 10)}{x^{2} (y^{4} \cdot 6)}$

Step 7.2.3

Rewrite the expression.

$\frac{x^{3} y^{7} \cdot 10}{y^{4} \cdot 6}$

Step 8

Cancel the common factor of $y^{7}$ and $y^{4}$ .

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Step 8.1

Factor $y^{4}$ out of $x^{3} y^{7} \cdot 10$ .

$\frac{y^{4} (x^{3} y^{3} \cdot 10)}{y^{4} \cdot 6}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

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

$\frac{y^{4} (x^{3} y^{3} \cdot 10)}{y^{4} (6)}$

Step 8.2.2

Cancel the common factor.

$\frac{y^{4} (x^{3} y^{3} \cdot 10)}{y^{4} \cdot 6}$

Step 8.2.3

Rewrite the expression.

$\frac{x^{3} y^{3} \cdot 10}{6}$

Step 9

Cancel the common factor of $10$ and $6$ .

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Step 9.1

Factor $2$ out of $x^{3} y^{3} \cdot 10$ .

$\frac{2 (x^{3} y^{3} \cdot 5)}{6}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $2$ out of $6$ .

$\frac{2 (x^{3} y^{3} \cdot 5)}{2 (3)}$

Step 9.2.2

Cancel the common factor.

$\frac{2 (x^{3} y^{3} \cdot 5)}{2 \cdot 3}$

Step 9.2.3

Rewrite the expression.

$\frac{x^{3} y^{3} \cdot 5}{3}$

Step 10

Move $5$ to the left of $x^{3} y^{3}$ .

$\frac{5 x^{3} y^{3}}{3}$