Evaluate 2/3(9)^(3/2)

$\frac{2}{3} {(9)}^{\frac{3}{2}}$

Step 1

Simplify the expression.

Rewrite $9$ as $3^{2}$ .

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

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

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

Step 2

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

$\frac{2}{3} \cdot 27$

Step 4

Cancel the common factor of $3$ .

Factor $3$ out of $27$ .

$\frac{2}{3} \cdot (3 (9))$

Cancel the common factor.

$\frac{2}{3} \cdot (3 \cdot 9)$

Rewrite the expression.

$2 \cdot 9$

Step 5

Multiply $2$ by $9$ .

$18$