Algebra Examples

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

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{x^{2} y^{2}}{m} \cdot \frac{\frac{x y}{m^{2}} \div \frac{y m}{x^{2}}}{\frac{x^{2} m^{2}}{y} \div \frac{y^{2} m^{2}}{x} \cdot \frac{x m}{y^{2}}}$

Step 2

Combine.

$\frac{x^{2} y^{2} \frac{x y}{m^{2}} \div \frac{y m}{x^{2}}}{m \frac{x^{2} m^{2}}{y} \div \frac{y^{2} m^{2}}{x} \cdot \frac{x m}{y^{2}}}$

Step 3

Multiply $\frac{y^{2} m^{2}}{x}$ by $\frac{x m}{y^{2}}$ .

$\frac{x^{2} y^{2} \frac{x y}{m^{2}} \div \frac{y m}{x^{2}}}{m \frac{x^{2} m^{2}}{y} \div \frac{y^{2} m^{2} (x m)}{x y^{2}}}$

Step 4

Simplify the numerator.

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Step 4.1

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

$\frac{x^{2} y^{2} \frac{x y}{m^{2}} \div \frac{y m}{x^{2}}}{m \frac{x^{2} m^{2}}{y} \div \frac{y^{2} (m^{1} m^{2}) x}{x y^{2}}}$

Step 4.2

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

$\frac{x^{2} y^{2} \frac{x y}{m^{2}} \div \frac{y m}{x^{2}}}{m \frac{x^{2} m^{2}}{y} \div \frac{y^{2} m^{1 + 2} x}{x y^{2}}}$

Step 4.3

Add $1$ and $2$ .

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

Step 5

Simplify the denominator.

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Step 5.1

Reduce the expression $\frac{y^{2} m^{3} x}{x y^{2}}$ by cancelling the common factors.

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

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

Step 5.2

Cancel the common factor of $x$ .

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Step 5.2.1

Cancel the common factor.

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

Step 5.2.2

Divide $m^{3}$ by $1$ .

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

Step 6

Simplify the numerator.

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Step 6.1

Combine $x^{2}$ and $\frac{x y}{m^{2}} \div \frac{y m}{x^{2}}$ .

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

Step 6.2

Combine $y^{2}$ and $\frac{x^{2} \frac{x y}{m^{2}}}{\frac{y m}{x^{2}}}$ .

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

Step 7

Combine $m$ and $\frac{x^{2} m^{2}}{y} \div m^{3}$ .

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

Step 8

Simplify the numerator.

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Step 8.1

Combine $y^{2}$ and $\frac{x y}{m^{2}}$ .

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

Step 8.2

Combine $x^{2}$ and $\frac{y^{2} (x y)}{m^{2}}$ .

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

Step 9

Simplify the numerator.

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Step 9.1

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

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Step 9.1.1

Move $x$ .

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

Step 9.1.2

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

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Step 9.1.2.1

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

$\frac{\frac{\frac{x^{1} x^{2} (y^{2} (y))}{m^{2}}}{\frac{y m}{x^{2}}}}{\frac{m \frac{x^{2} m^{2}}{y}}{m^{3}}}$

Step 9.1.2.2

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

$\frac{\frac{\frac{x^{1 + 2} (y^{2} (y))}{m^{2}}}{\frac{y m}{x^{2}}}}{\frac{m \frac{x^{2} m^{2}}{y}}{m^{3}}}$

Step 9.1.3

Add $1$ and $2$ .

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

Step 9.2

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

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Step 9.2.1

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

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Step 9.2.1.1

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

$\frac{\frac{\frac{x^{3} (y^{2} y^{1})}{m^{2}}}{\frac{y m}{x^{2}}}}{\frac{m \frac{x^{2} m^{2}}{y}}{m^{3}}}$

Step 9.2.1.2

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

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

Step 9.2.2

Add $2$ and $1$ .

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

Step 10

Combine $m$ and $\frac{x^{2} m^{2}}{y}$ .

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

Step 11

Simplify the numerator.

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Step 11.1

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

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

Step 11.2

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

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

Step 11.3

Add $2$ and $1$ .

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

Step 12

Simplify the numerator.

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Step 12.1

Multiply the numerator by the reciprocal of the denominator.

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

Step 12.2

Combine.

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

Step 12.3

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

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Step 12.3.1

Move $x^{2}$ .

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

Step 12.3.2

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

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

Step 12.3.3

Add $2$ and $3$ .

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

Step 12.4

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

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Step 12.4.1

Move $m$ .

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

Step 12.4.2

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

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Step 12.4.2.1

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

$\frac{\frac{x^{5} y^{3}}{m^{1} m^{2} y}}{\frac{\frac{m^{3} x^{2}}{y}}{m^{3}}}$

Step 12.4.2.2

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

$\frac{\frac{x^{5} y^{3}}{m^{1 + 2} y}}{\frac{\frac{m^{3} x^{2}}{y}}{m^{3}}}$

Step 12.4.3

Add $1$ and $2$ .

$\frac{\frac{x^{5} y^{3}}{m^{3} y}}{\frac{\frac{m^{3} x^{2}}{y}}{m^{3}}}$

Step 12.5

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

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Step 12.5.1

Factor $y$ out of $x^{5} y^{3}$ .

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

Step 12.5.2

Cancel the common factors.

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Step 12.5.2.1

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

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

Step 12.5.2.2

Cancel the common factor.

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

Step 12.5.2.3

Rewrite the expression.

$\frac{\frac{x^{5} y^{2}}{m^{3}}}{\frac{\frac{m^{3} x^{2}}{y}}{m^{3}}}$

Step 13

Simplify the denominator.

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Step 13.1

Multiply the numerator by the reciprocal of the denominator.

$\frac{\frac{x^{5} y^{2}}{m^{3}}}{\frac{m^{3} x^{2}}{y} \cdot \frac{1}{m^{3}}}$

Step 13.2

Combine.

$\frac{\frac{x^{5} y^{2}}{m^{3}}}{\frac{m^{3} x^{2} \cdot 1}{y m^{3}}}$

Step 13.3

Cancel the common factor of $m^{3}$ .

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Step 13.3.1

Cancel the common factor.

$\frac{\frac{x^{5} y^{2}}{m^{3}}}{\frac{m^{3} x^{2} \cdot 1}{y m^{3}}}$

Step 13.3.2

Rewrite the expression.

$\frac{\frac{x^{5} y^{2}}{m^{3}}}{\frac{x^{2} \cdot 1}{y}}$

Step 13.4

Multiply $x^{2}$ by $1$ .

$\frac{\frac{x^{5} y^{2}}{m^{3}}}{\frac{x^{2}}{y}}$

Step 14

Multiply the numerator by the reciprocal of the denominator.

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

Step 15

Combine.

$\frac{x^{5} y^{2} y}{m^{3} x^{2}}$

Step 16

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

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Step 16.1

Move $y$ .

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

Step 16.2

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

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Step 16.2.1

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

$\frac{x^{5} (y^{1} y^{2})}{m^{3} x^{2}}$

Step 16.2.2

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

$\frac{x^{5} y^{1 + 2}}{m^{3} x^{2}}$

Step 16.3

Add $1$ and $2$ .

$\frac{x^{5} y^{3}}{m^{3} x^{2}}$

Step 17

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

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Step 17.1

Factor $x^{2}$ out of $x^{5} y^{3}$ .

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

Step 17.2

Cancel the common factors.

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Step 17.2.1

Factor $x^{2}$ out of $m^{3} x^{2}$ .

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

Step 17.2.2

Cancel the common factor.

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

Step 17.2.3

Rewrite the expression.

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