Basic Math Examples

$(\frac{4}{3}) {(2)}^{\frac{3}{2}}$

Step 1

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

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

Step 2

Rewrite $4$ as $2^{2}$ .

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Combine the numerators over the common denominator.

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

Step 7

Simplify the numerator.

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Step 7.1

Multiply $2$ by $2$ .

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

Step 7.2

Add $4$ and $3$ .

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

Step 8

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$3.77123616 \dots$