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

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

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

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

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

$8 {(a^{\frac{1}{2}})}^{3} {(b^{\frac{1}{3}})}^{3}$

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

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

$8 a^{\frac{1}{2} \cdot 3} {(b^{\frac{1}{3}})}^{3}$

Combine $\frac{1}{2}$ and $3$ .

$8 a^{\frac{3}{2}} {(b^{\frac{1}{3}})}^{3}$

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

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

$8 a^{\frac{3}{2}} b^{\frac{1}{3} \cdot 3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 a^{\frac{3}{2}} b^{\frac{1}{3} \cdot 3}$

Rewrite the expression.

$8 a^{\frac{3}{2}} b^{1}$

Simplify.

$8 a^{\frac{3}{2}} b$

Reorder factors in $8 a^{\frac{3}{2}} b$ .

$8 b a^{\frac{3}{2}}$