Simplify (a^(2/3)b^(1/3))^(1/2)

${(a^{\frac{2}{3}} b^{\frac{1}{3}})}^{\frac{1}{2}}$

Apply the product rule to $a^{\frac{2}{3}} b^{\frac{1}{3}}$ .

${(a^{\frac{2}{3}})}^{\frac{1}{2}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Multiply the exponents in ${(a^{\frac{2}{3}})}^{\frac{1}{2}}$ .

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

$a^{\frac{2}{3} \cdot \frac{1}{2}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$a^{\frac{2}{3} \cdot \frac{1}{2}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Rewrite the expression.

$a^{\frac{1}{3}} {(b^{\frac{1}{3}})}^{\frac{1}{2}}$

Multiply the exponents in ${(b^{\frac{1}{3}})}^{\frac{1}{2}}$ .

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

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

Multiply $\frac{1}{3} \cdot \frac{1}{2}$ .

Multiply $\frac{1}{3}$ by $\frac{1}{2}$ .

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

Multiply $3$ by $2$ .

$a^{\frac{1}{3}} b^{\frac{1}{6}}$