Evaluate (3^(2/3))^(5/2)

${(3^{\frac{2}{3}})}^{\frac{5}{2}}$

Step 1

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

$3^{\frac{2}{3} \cdot \frac{5}{2}}$

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

$3^{\frac{2}{3} \cdot \frac{5}{2}}$

Rewrite the expression.

$3^{\frac{1}{3} \cdot 5}$

Step 3

Combine $\frac{1}{3}$ and $5$ .

$3^{\frac{5}{3}}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$3^{\frac{5}{3}}$

Decimal Form:

$6.24025146 \dots$