Algebra Examples

$2^{\frac{1}{2}} \cdot 2^{3}$

Step 1

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

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

Step 2

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

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

Step 3

Combine $3$ and $\frac{2}{2}$ .

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

Step 4

Combine the numerators over the common denominator.

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

Step 5

Simplify the numerator.

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Step 5.1

Multiply $3$ by $2$ .

$2^{\frac{1 + 6}{2}}$

Step 5.2

Add $1$ and $6$ .

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