Evaluate (6^(1/2)*4^(1/3))^2

${(6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}})}^{2}$

Apply the product rule to $6^{\frac{1}{2}} \cdot 4^{\frac{1}{3}}$ .

${(6^{\frac{1}{2}})}^{2} \cdot {(4^{\frac{1}{3}})}^{2}$

Multiply the exponents in ${(6^{\frac{1}{2}})}^{2}$ .

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

$6^{\frac{1}{2} \cdot 2} \cdot {(4^{\frac{1}{3}})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$6^{\frac{1}{2} \cdot 2} \cdot {(4^{\frac{1}{3}})}^{2}$

Rewrite the expression.

$6^{1} \cdot {(4^{\frac{1}{3}})}^{2}$

Evaluate the exponent.

$6 \cdot {(4^{\frac{1}{3}})}^{2}$

Multiply the exponents in ${(4^{\frac{1}{3}})}^{2}$ .

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

$6 \cdot 4^{\frac{1}{3} \cdot 2}$

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

$6 \cdot 4^{\frac{2}{3}}$

The result can be shown in multiple forms.

Exact Form:

$6 \cdot 4^{\frac{2}{3}}$

Decimal Form:

$15.11905259 \dots$