Algebra Examples

$\frac{5 x}{2 y} \cdot \frac{2 x}{5 y} \cdot \frac{3 x}{2}$

Step 1

Cancel the common factor of $5$ .

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Step 1.1

Factor $5$ out of $5 x$ .

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

Step 1.2

Factor $5$ out of $5 y$ .

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

Step 1.3

Cancel the common factor.

$\frac{5 x}{2 y} \cdot \frac{2 x}{5 y} \cdot \frac{3 x}{2}$

Step 1.4

Rewrite the expression.

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

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Factor $2$ out of $2 y$ .

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

Step 2.2

Factor $2$ out of $2 x$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

Multiply $\frac{x}{y}$ by $\frac{x}{y}$ .

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

Step 4

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

$\frac{x^{1} x}{y \cdot y} \cdot \frac{3 x}{2}$

Step 5

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

$\frac{x^{1} x^{1}}{y \cdot y} \cdot \frac{3 x}{2}$

Step 6

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

$\frac{x^{1 + 1}}{y \cdot y} \cdot \frac{3 x}{2}$

Step 7

Add $1$ and $1$ .

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

Step 8

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

$\frac{x^{2}}{y^{1} y} \cdot \frac{3 x}{2}$

Step 9

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

$\frac{x^{2}}{y^{1} y^{1}} \cdot \frac{3 x}{2}$

Step 10

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

$\frac{x^{2}}{y^{1 + 1}} \cdot \frac{3 x}{2}$

Step 11

Add $1$ and $1$ .

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

Step 12

Combine.

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

Step 13

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

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Step 13.1

Move $x$ .

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

Step 13.2

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

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Step 13.2.1

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

$\frac{x^{1} x^{2} \cdot 3}{y^{2} \cdot 2}$

Step 13.2.2

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

$\frac{x^{1 + 2} \cdot 3}{y^{2} \cdot 2}$

Step 13.3

Add $1$ and $2$ .

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

Step 14

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

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

Step 15

Move $2$ to the left of $y^{2}$ .

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