Evaluate 2/3(4)^(3/2)

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

Step 1

Simplify the expression.

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

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

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

Raise $2$ to the power of $3$ .

$\frac{2}{3} \cdot 8$

Step 4

Multiply $\frac{2}{3} \cdot 8$ .

Combine $\frac{2}{3}$ and $8$ .

$\frac{2 \cdot 8}{3}$

Multiply $2$ by $8$ .

$\frac{16}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{16}{3}$

Decimal Form:

$5.\overline{3}$

Mixed Number Form:

$5 \frac{1}{3}$