Algebra Examples

$\frac{x^{1} y^{11} y^{- 13}}{x^{5}}$

Step 1

Multiply $y^{11}$ by $y^{- 13}$ by adding the exponents.

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Step 1.1

Move $y^{- 13}$ .

$\frac{x^{1} (y^{- 13} y^{11})}{x^{5}}$

Step 1.2

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

$\frac{x^{1} y^{- 13 + 11}}{x^{5}}$

Step 1.3

Add $- 13$ and $11$ .

$\frac{x^{1} y^{- 2}}{x^{5}}$

Step 2

Simplify the expression.

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Step 2.1

Simplify $x^{1} y^{- 2}$ .

$\frac{x y^{- 2}}{x^{5}}$

Step 2.2

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

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

Step 3

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

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factors.

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Step 3.3.1

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

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

Step 3.3.2

Cancel the common factor.

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

Step 3.3.3

Rewrite the expression.

$\frac{1}{x^{4} y^{2}}$