Precalculus Examples

$x^{\frac{1}{2}} x^{\frac{1}{7}}$

Step 1

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

$x^{\frac{1}{2} + \frac{1}{7}}$

Step 2

To write $\frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$x^{\frac{1}{2} \cdot \frac{7}{7} + \frac{1}{7}}$

Step 3

To write $\frac{1}{7}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x^{\frac{1}{2} \cdot \frac{7}{7} + \frac{1}{7} \cdot \frac{2}{2}}$

Step 4

Write each expression with a common denominator of $14$ , by multiplying each by an appropriate factor of $1$ .

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Step 4.1

Multiply $\frac{1}{2}$ by $\frac{7}{7}$ .

$x^{\frac{7}{2 \cdot 7} + \frac{1}{7} \cdot \frac{2}{2}}$

Step 4.2

Multiply $2$ by $7$ .

$x^{\frac{7}{14} + \frac{1}{7} \cdot \frac{2}{2}}$

Step 4.3

Multiply $\frac{1}{7}$ by $\frac{2}{2}$ .

$x^{\frac{7}{14} + \frac{2}{7 \cdot 2}}$

Step 4.4

Multiply $7$ by $2$ .

$x^{\frac{7}{14} + \frac{2}{14}}$

Step 5

Combine the numerators over the common denominator.

$x^{\frac{7 + 2}{14}}$

Step 6

Add $7$ and $2$ .

$x^{\frac{9}{14}}$