Algebra Examples

$\frac{x^{\frac{1}{4}} y}{x^{\frac{3}{4}} y^{\frac{1}{2}}}$

Step 1

Move $x^{\frac{1}{4}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{y}{x^{\frac{3}{4}} y^{\frac{1}{2}} x^{- \frac{1}{4}}}$

Step 2

Multiply $x^{\frac{3}{4}}$ by $x^{- \frac{1}{4}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{1}{4}}$ .

$\frac{y}{x^{- \frac{1}{4}} x^{\frac{3}{4}} y^{\frac{1}{2}}}$

Step 2.2

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

$\frac{y}{x^{- \frac{1}{4} + \frac{3}{4}} y^{\frac{1}{2}}}$

Step 2.3

Combine the numerators over the common denominator.

$\frac{y}{x^{\frac{- 1 + 3}{4}} y^{\frac{1}{2}}}$

Step 2.4

Add $- 1$ and $3$ .

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

Step 2.5

Cancel the common factor of $2$ and $4$ .

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Step 2.5.1

Factor $2$ out of $2$ .

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

Step 2.5.2

Cancel the common factors.

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Step 2.5.2.1

Factor $2$ out of $4$ .

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

Step 2.5.2.2

Cancel the common factor.

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

Step 2.5.2.3

Rewrite the expression.

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

Step 3

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

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

Step 4

Multiply $y$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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Step 4.1

Multiply $y$ by $y^{- \frac{1}{2}}$ .

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Step 4.1.1

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

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

Step 4.1.2

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

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

Step 4.2

Write $1$ as a fraction with a common denominator.

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

Step 4.3

Combine the numerators over the common denominator.

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

Step 4.4

Subtract $1$ from $2$ .

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