Algebra Examples

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

Step 1

Move $x^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

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

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Step 2.1

Move $x^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

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

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Step 3.1

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

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

Step 3.2

Factor $y$ out of $y^{1}$ .

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

Step 3.3

Cancel the common factors.

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Step 3.3.1

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

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

Step 3.3.2

Cancel the common factor.

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

Step 3.3.3

Rewrite the expression.

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