Algebra Examples

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

Step 1

Multiply

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

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

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Step 1.1

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Step 1.2

Move the negative in front of the fraction.

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

Step 1.3

To write

$\frac{1}{2}$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

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

Step 1.4

Write each expression with a common denominator of

$4$ , by multiplying each by an appropriate factor of

$1$ .

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Step 1.4.1

Multiply

$\frac{1}{2}$ by

$\frac{2}{2}$ .

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

Step 1.4.2

Multiply

$2$ by

$2$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Subtract

$3$ from

$2$ .

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

Step 1.7

Move the negative in front of the fraction.

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

Step 2

Move

$x^{- \frac{1}{4}}$ to the denominator using the negative exponent rule

$b^{- n} = \frac{1}{b^{n}}$ .

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

Step 3

Multiply

$x^{\frac{1}{4}}$ by

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

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Step 3.1

Use the power rule

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{x^{\frac{1}{4} + \frac{1}{4}}}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{1 + 1}{4}}}$

Step 3.3

Add

$1$ and

$1$ .

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

Step 3.4

Cancel the common factor of

$2$ and

$4$ .

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Step 3.4.1

Factor

$2$ out of

$2$ .

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

Step 3.4.2

Cancel the common factors.

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Step 3.4.2.1

Factor

$2$ out of

$4$ .

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

Step 3.4.2.2

Cancel the common factor.

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

Step 3.4.2.3

Rewrite the expression.

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