Precalculus Examples

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

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

Step 1

Use the power rule

a^{m} a^{n} = a^{m + n}

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

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

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

Step 2

To write

\frac{3}{2}

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

\frac{7}{7}

$\frac{7}{7}$ .

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

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

Step 3

To write

\frac{2}{7}

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

\frac{2}{2}

$\frac{2}{2}$ .

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

$14$ , by multiplying each by an appropriate factor of

1

$1$ .

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Step 4.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{7}{7}

$\frac{7}{7}$ .

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

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

Step 4.2

Multiply

2

$2$ by

7

$7$ .

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

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

Step 4.3

Multiply

\frac{2}{7}

$\frac{2}{7}$ by

\frac{2}{2}

$\frac{2}{2}$ .

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

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

Step 4.4

Multiply

7

$7$ by

2

$2$ .

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

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

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

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

Step 5

Combine the numerators over the common denominator.

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

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

Step 6

Simplify the numerator.

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Step 6.1

Multiply

3

$3$ by

7

$7$ .

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

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

Step 6.2

Multiply

2

$2$ by

2

$2$ .

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

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

Step 6.3

Add

21

$21$ and

4

$4$ .

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

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

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

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