Algebra Examples

$\frac{12 x y}{7 x^{4}} \cdot \frac{7 x^{5} y^{2}}{4 y}$

Step 1

Combine.

$\frac{12 x y (7 x^{5} y^{2})}{7 x^{4} (4 y)}$

Step 2

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

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Step 2.1

Move $x^{5}$ .

$\frac{12 (x^{5} x) y (7 y^{2})}{7 x^{4} (4 y)}$

Step 2.2

Multiply $x^{5}$ by $x$ .

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Step 2.2.1

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

$\frac{12 (x^{5} x^{1}) y (7 y^{2})}{7 x^{4} (4 y)}$

Step 2.2.2

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

$\frac{12 x^{5 + 1} y (7 y^{2})}{7 x^{4} (4 y)}$

Step 2.3

Add $5$ and $1$ .

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

Step 3

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

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Step 3.1

Move $y^{2}$ .

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

Step 3.2

Multiply $y^{2}$ by $y$ .

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Step 3.2.1

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

$\frac{12 x^{6} (y^{2} y^{1}) \cdot 7}{7 x^{4} (4 y)}$

Step 3.2.2

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

$\frac{12 x^{6} y^{2 + 1} \cdot 7}{7 x^{4} (4 y)}$

Step 3.3

Add $2$ and $1$ .

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

Step 4

Cancel the common factor of $12$ and $4$ .

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Step 4.1

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

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

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $4$ out of $7 x^{4} (4 y)$ .

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

Step 4.2.2

Cancel the common factor.

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

Step 4.2.3

Rewrite the expression.

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

Step 5

Cancel the common factor of $x^{6}$ and $x^{4}$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $x^{4}$ out of $7 x^{4} (y)$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 6

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

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Step 6.1

Factor $y$ out of $3 x^{2} y^{3} \cdot 7$ .

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

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $y$ out of $7 (y)$ .

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

Step 6.2.2

Cancel the common factor.

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

Step 6.2.3

Rewrite the expression.

$\frac{3 x^{2} y^{2} \cdot 7}{7}$

Step 7

Cancel the common factor of $7$ .

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Step 7.1

Cancel the common factor.

$\frac{3 x^{2} y^{2} \cdot 7}{7}$

Step 7.2

Divide $3 x^{2} y^{2}$ by $1$ .

$3 x^{2} y^{2}$