Calculus Examples

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

Step 1

Multiply $2^{\frac{1}{2}}$ by $2^{\frac{3}{2}}$ by adding the exponents.

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Step 1.1

Move $2^{\frac{3}{2}}$ .

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

Step 1.2

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

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

Step 1.3

Combine the numerators over the common denominator.

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

Step 1.4

Add $3$ and $1$ .

$2^{\frac{4}{2}} \cdot \frac{2}{3}$

Step 1.5

Divide $4$ by $2$ .

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

Step 2

Raise $2$ to the power of $2$ .

$4 \cdot \frac{2}{3}$

Step 3

Multiply $4 (\frac{2}{3})$ .

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Step 3.1

Combine $4$ and $\frac{2}{3}$ .

$\frac{4 \cdot 2}{3}$

Step 3.2

Multiply $4$ by $2$ .

$\frac{8}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{8}{3}$

Decimal Form:

$2.\overline{6}$

Mixed Number Form:

$2 \frac{2}{3}$