Algebra Examples

$\frac{12 x^{10} y^{4}}{8 x^{3} y^{10}} \cdot \frac{6 x^{4} y^{2}}{x}$

Step 1

Combine.

$\frac{12 x^{10} y^{4} (6 x^{4} y^{2})}{8 x^{3} y^{10} x}$

Step 2

Multiply $x^{10}$ by $x^{4}$ by adding the exponents.

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Step 2.1

Move $x^{4}$ .

$\frac{12 (x^{4} x^{10}) y^{4} (6 y^{2})}{8 x^{3} y^{10} x}$

Step 2.2

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

$\frac{12 x^{4 + 10} y^{4} (6 y^{2})}{8 x^{3} y^{10} x}$

Step 2.3

Add $4$ and $10$ .

$\frac{12 x^{14} y^{4} (6 y^{2})}{8 x^{3} y^{10} x}$

Step 3

Multiply $y^{4}$ by $y^{2}$ by adding the exponents.

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Step 3.1

Move $y^{2}$ .

$\frac{12 x^{14} (y^{2} y^{4}) \cdot 6}{8 x^{3} y^{10} x}$

Step 3.2

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

$\frac{12 x^{14} y^{2 + 4} \cdot 6}{8 x^{3} y^{10} x}$

Step 3.3

Add $2$ and $4$ .

$\frac{12 x^{14} y^{6} \cdot 6}{8 x^{3} y^{10} x}$

Step 4

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

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Step 4.1

Move $x$ .

$\frac{12 x^{14} y^{6} \cdot 6}{8 (x \cdot x^{3}) y^{10}}$

Step 4.2

Multiply $x$ by $x^{3}$ .

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Step 4.2.1

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

$\frac{12 x^{14} y^{6} \cdot 6}{8 (x^{1} x^{3}) y^{10}}$

Step 4.2.2

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

$\frac{12 x^{14} y^{6} \cdot 6}{8 x^{1 + 3} y^{10}}$

Step 4.3

Add $1$ and $3$ .

$\frac{12 x^{14} y^{6} \cdot 6}{8 x^{4} y^{10}}$

Step 5

Cancel the common factor of $12$ and $8$ .

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Step 5.1

Factor $4$ out of $12 x^{14} y^{6} \cdot 6$ .

$\frac{4 (3 x^{14} y^{6} \cdot 6)}{8 x^{4} y^{10}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

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

$\frac{4 (3 x^{14} y^{6} \cdot 6)}{4 (2 x^{4} y^{10})}$

Step 5.2.2

Cancel the common factor.

$\frac{4 (3 x^{14} y^{6} \cdot 6)}{4 (2 x^{4} y^{10})}$

Step 5.2.3

Rewrite the expression.

$\frac{3 x^{14} y^{6} \cdot 6}{2 x^{4} y^{10}}$

Step 6

Cancel the common factor of $x^{14}$ and $x^{4}$ .

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Step 6.1

Factor $x^{4}$ out of $3 x^{14} y^{6} \cdot 6$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

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

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

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

Step 7

Cancel the common factor of $y^{6}$ and $y^{10}$ .

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Step 7.1

Factor $y^{6}$ out of $3 x^{10} y^{6} \cdot 6$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $y^{6}$ out of $2 y^{10}$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

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

Step 8

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

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Step 8.1

Factor $2$ out of $3 x^{10} \cdot 6$ .

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

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $2$ out of $2 y^{4}$ .

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

Step 8.2.2

Cancel the common factor.

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

Step 8.2.3

Rewrite the expression.

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

Step 9

Multiply $3$ by $3$ .

$\frac{9 x^{10}}{y^{4}}$