Algebra Examples

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

Step 1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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Step 1.4.1

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

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

Step 1.4.2

Multiply $4$ by $3$ .

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

Step 1.4.3

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

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

Step 1.4.4

Multiply $6$ by $2$ .

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

Step 1.5

Combine the numerators over the common denominator.

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

Step 1.6

Add $3$ and $2$ .

$x^{\frac{5}{12}} \cdot x^{\frac{1}{3}}$

Step 2

Multiply $x^{\frac{5}{12}}$ by $x^{\frac{1}{3}}$ by adding the exponents.

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Step 2.1

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

$x^{\frac{5}{12} + \frac{1}{3}}$

Step 2.2

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

$x^{\frac{5}{12} + \frac{1}{3} \cdot \frac{4}{4}}$

Step 2.3

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

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Step 2.3.1

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

$x^{\frac{5}{12} + \frac{4}{3 \cdot 4}}$

Step 2.3.2

Multiply $3$ by $4$ .

$x^{\frac{5}{12} + \frac{4}{12}}$

Step 2.4

Combine the numerators over the common denominator.

$x^{\frac{5 + 4}{12}}$

Step 2.5

Add $5$ and $4$ .

$x^{\frac{9}{12}}$

Step 2.6

Cancel the common factor of $9$ and $12$ .

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Step 2.6.1

Factor $3$ out of $9$ .

$x^{\frac{3 (3)}{12}}$

Step 2.6.2

Cancel the common factors.

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Step 2.6.2.1

Factor $3$ out of $12$ .

$x^{\frac{3 \cdot 3}{3 \cdot 4}}$

Step 2.6.2.2

Cancel the common factor.

$x^{\frac{3 \cdot 3}{3 \cdot 4}}$

Step 2.6.2.3

Rewrite the expression.

$x^{\frac{3}{4}}$