Precalculus Examples

$u^{\frac{3}{2}} u^{\frac{2}{7}}$

Step 1

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

$u^{\frac{3}{2} + \frac{2}{7}}$

Step 2

To write $\frac{3}{2}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$u^{\frac{3}{2} \cdot \frac{7}{7} + \frac{2}{7}}$

Step 3

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

$u^{\frac{3}{2} \cdot \frac{7}{7} + \frac{2}{7} \cdot \frac{2}{2}}$

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 $\frac{3}{2}$ by $\frac{7}{7}$ .

$u^{\frac{3 \cdot 7}{2 \cdot 7} + \frac{2}{7} \cdot \frac{2}{2}}$

Step 4.2

Multiply $2$ by $7$ .

$u^{\frac{3 \cdot 7}{14} + \frac{2}{7} \cdot \frac{2}{2}}$

Step 4.3

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

$u^{\frac{3 \cdot 7}{14} + \frac{2 \cdot 2}{7 \cdot 2}}$

Step 4.4

Multiply $7$ by $2$ .

$u^{\frac{3 \cdot 7}{14} + \frac{2 \cdot 2}{14}}$

Step 5

Combine the numerators over the common denominator.

$u^{\frac{3 \cdot 7 + 2 \cdot 2}{14}}$

Step 6

Simplify the numerator.

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Step 6.1

Multiply $3$ by $7$ .

$u^{\frac{21 + 2 \cdot 2}{14}}$

Step 6.2

Multiply $2$ by $2$ .

$u^{\frac{21 + 4}{14}}$

Step 6.3

Add $21$ and $4$ .

$u^{\frac{25}{14}}$