Answer:
[tex] \sqrt[3]{6} [/tex]
Step-by-step explanation:
To convert the expression [tex] (6^{\frac{2}{3}})^{\frac{1}{2}} [/tex] from rational exponent form to radical form, you can use the property that [tex] (a^b)^c = a^{b \cdot c} [/tex]. Applying this property, we can simplify the given expression:
[tex] (6^{\frac{2}{3}})^{\frac{1}{2}} = 6^{\frac{2}{3} \cdot \frac{1}{2}} [/tex]
Now, multiply the exponents:
[tex] 6^{\frac{1}{3}} [/tex]
The exponent [tex] \frac{1}{3} [/tex] represents the cube root. Therefore, the expression becomes:
[tex] \sqrt[3]{6} [/tex]
Thus, the expression [tex] (6^{\frac{2}{3}})^{\frac{1}{2}} [/tex] in radical form is:
[tex] \sqrt[3]{6} [/tex]
