Pre-Algebra Examples

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

Step 1

Multiply $x^{\frac{1}{3}}$ by $x^{- \frac{1}{2}}$ 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.

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

Step 1.2

To write $\frac{1}{3}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

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

Step 1.4

Write each expression with a common denominator of $6$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.4.1

Multiply $\frac{1}{3}$ by $\frac{2}{2}$ .

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

Step 1.4.2

Multiply $3$ by $2$ .

$\frac{x^{\frac{2}{6} - \frac{1}{2} \cdot \frac{3}{3}}}{x^{\frac{1}{4}}}$

Step 1.4.3

Multiply $\frac{1}{2}$ by $\frac{3}{3}$ .

$\frac{x^{\frac{2}{6} - \frac{3}{2 \cdot 3}}}{x^{\frac{1}{4}}}$

Step 1.4.4

Multiply $2$ by $3$ .

$\frac{x^{\frac{2}{6} - \frac{3}{6}}}{x^{\frac{1}{4}}}$

Step 1.5

Combine the numerators over the common denominator.

$\frac{x^{\frac{2 - 3}{6}}}{x^{\frac{1}{4}}}$

Step 1.6

Subtract $3$ from $2$ .

$\frac{x^{\frac{- 1}{6}}}{x^{\frac{1}{4}}}$

Step 1.7

Move the negative in front of the fraction.

$\frac{x^{- \frac{1}{6}}}{x^{\frac{1}{4}}}$

Step 2

Move $x^{- \frac{1}{6}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{x^{\frac{1}{4}} x^{\frac{1}{6}}}$

Step 3

Multiply $x^{\frac{1}{4}}$ by $x^{\frac{1}{6}}$ 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.

$\frac{1}{x^{\frac{1}{4} + \frac{1}{6}}}$

Step 3.2

To write $\frac{1}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{1}{x^{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6}}}$

Step 3.3

To write $\frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{1}{x^{\frac{1}{4} \cdot \frac{3}{3} + \frac{1}{6} \cdot \frac{2}{2}}}$

Step 3.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 3.4.1

Multiply $\frac{1}{4}$ by $\frac{3}{3}$ .

$\frac{1}{x^{\frac{3}{4 \cdot 3} + \frac{1}{6} \cdot \frac{2}{2}}}$

Step 3.4.2

Multiply $4$ by $3$ .

$\frac{1}{x^{\frac{3}{12} + \frac{1}{6} \cdot \frac{2}{2}}}$

Step 3.4.3

Multiply $\frac{1}{6}$ by $\frac{2}{2}$ .

$\frac{1}{x^{\frac{3}{12} + \frac{2}{6 \cdot 2}}}$

Step 3.4.4

Multiply $6$ by $2$ .

$\frac{1}{x^{\frac{3}{12} + \frac{2}{12}}}$

Step 3.5

Combine the numerators over the common denominator.

$\frac{1}{x^{\frac{3 + 2}{12}}}$

Step 3.6

Add $3$ and $2$ .

$\frac{1}{x^{\frac{5}{12}}}$