Answer:
[tex]\sqrt[3]{32x^5} [/tex]
Step-by-step explanation:
To convert the expression [tex](2x)^{\frac{5}{3}}[/tex] from rational exponent form to radical form, we recall that [tex]a^{\frac{m}{n}}[/tex] is equivalent to the [tex]n[/tex]-th root of [tex]a^m[/tex].
Therefore, we can express [tex](2x)^{\frac{5}{3}}[/tex] as the cube root of [tex](2x)^5[/tex]:
[tex] (2x)^{\frac{5}{3}} = \sqrt[3]{(2x)^5} [/tex]
Now, to simplify [tex](2x)^5[/tex], we apply the power rule for exponents which states that [tex](a^m)^n = a^{m \cdot n}[/tex]:
[tex] (2x)^5 = 2^5 \cdot x^5 = 32x^5 [/tex]
So, the expression becomes:
[tex] \sqrt[3]{32x^5} [/tex]
Therefore, the expression [tex](2x)^{\frac{5}{3}}[/tex] in radical form is:
[tex]\sqrt[3]{32x^5} \textsf{ or } \sqrt[3]{(2x)^5}[/tex]
