Algebra Examples

$\frac{14 x^{5} y^{3} \cdot 3 x^{4} y^{9}}{6 x^{3} y^{4}}$

Step 1

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

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Step 1.1

Move $x^{4}$ .

$\frac{14 (x^{4} x^{5}) y^{3} \cdot (3 y^{9})}{6 x^{3} y^{4}}$

Step 1.2

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

$\frac{14 x^{4 + 5} y^{3} \cdot (3 y^{9})}{6 x^{3} y^{4}}$

Step 1.3

Add $4$ and $5$ .

$\frac{14 x^{9} y^{3} \cdot (3 y^{9})}{6 x^{3} y^{4}}$

Step 2

Multiply $y^{3}$ by $y^{9}$ by adding the exponents.

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Step 2.1

Move $y^{9}$ .

$\frac{14 x^{9} (y^{9} y^{3}) \cdot 3}{6 x^{3} y^{4}}$

Step 2.2

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

$\frac{14 x^{9} y^{9 + 3} \cdot 3}{6 x^{3} y^{4}}$

Step 2.3

Add $9$ and $3$ .

$\frac{14 x^{9} y^{12} \cdot 3}{6 x^{3} y^{4}}$

Step 3

Cancel the common factor of $14$ and $6$ .

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Step 3.1

Factor $2$ out of $14 x^{9} y^{12} \cdot 3$ .

$\frac{2 (7 x^{9} y^{12} \cdot 3)}{6 x^{3} y^{4}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $6 x^{3} y^{4}$ .

$\frac{2 (7 x^{9} y^{12} \cdot 3)}{2 (3 x^{3} y^{4})}$

Step 3.2.2

Cancel the common factor.

$\frac{2 (7 x^{9} y^{12} \cdot 3)}{2 (3 x^{3} y^{4})}$

Step 3.2.3

Rewrite the expression.

$\frac{7 x^{9} y^{12} \cdot 3}{3 x^{3} y^{4}}$

Step 4

Cancel the common factor of $x^{9}$ and $x^{3}$ .

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Step 4.1

Factor $x^{3}$ out of $7 x^{9} y^{12} \cdot 3$ .

$\frac{x^{3} (7 x^{6} y^{12} \cdot 3)}{3 x^{3} y^{4}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $x^{3}$ out of $3 x^{3} y^{4}$ .

$\frac{x^{3} (7 x^{6} y^{12} \cdot 3)}{x^{3} (3 y^{4})}$

Step 4.2.2

Cancel the common factor.

$\frac{x^{3} (7 x^{6} y^{12} \cdot 3)}{x^{3} (3 y^{4})}$

Step 4.2.3

Rewrite the expression.

$\frac{7 x^{6} y^{12} \cdot 3}{3 y^{4}}$

Step 5

Cancel the common factor of $y^{12}$ and $y^{4}$ .

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Step 5.1

Factor $y^{4}$ out of $7 x^{6} y^{12} \cdot 3$ .

$\frac{y^{4} (7 x^{6} y^{8} \cdot 3)}{3 y^{4}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $y^{4}$ out of $3 y^{4}$ .

$\frac{y^{4} (7 x^{6} y^{8} \cdot 3)}{y^{4} \cdot 3}$

Step 5.2.2

Cancel the common factor.

$\frac{y^{4} (7 x^{6} y^{8} \cdot 3)}{y^{4} \cdot 3}$

Step 5.2.3

Rewrite the expression.

$\frac{7 x^{6} y^{8} \cdot 3}{3}$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Cancel the common factor.

$\frac{7 x^{6} y^{8} \cdot 3}{3}$

Step 6.2

Divide $7 x^{6} y^{8}$ by $1$ .

$7 x^{6} y^{8}$