Algebra Examples

$\frac{x^{6}}{x y^{- 5} y^{3}}$

Step 1

Multiply $y^{- 5}$ by $y^{3}$ by adding the exponents.

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Step 1.1

Move $y^{3}$ .

$\frac{x^{6}}{x (y^{3} y^{- 5})}$

Step 1.2

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

$\frac{x^{6}}{x y^{3 - 5}}$

Step 1.3

Subtract $5$ from $3$ .

$\frac{x^{6}}{x y^{- 2}}$

Step 2

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

$\frac{x^{6} y^{2}}{x}$

Step 3

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

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Step 3.1

Factor $x$ out of $x^{6} y^{2}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

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

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

Step 3.2.2

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

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

Divide $x^{5} y^{2}$ by $1$ .

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