Let's analyze the given expression and convert it to its radical form:
We are given the expression: [tex]\(\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{2}{5}}\)[/tex].
To convert an expression of the form [tex]\(x^{\frac{m}{n}}\)[/tex] to its radical form, we recognize that it is equivalent to the [tex]\(n\)[/tex]-th root of [tex]\(x\)[/tex] raised to the power of [tex]\(m\)[/tex], or [tex]\(\sqrt[n]{x^m}\)[/tex].
Here, [tex]\(x = 32 a^{10} b^{\frac{5}{2}}\)[/tex], [tex]\(m = 2\)[/tex], and [tex]\(n = 5\)[/tex].
Therefore, the expression [tex]\(\left(32 a^{10} b^{\frac{5}{2}}\right)^{\frac{2}{5}}\)[/tex] can be rewritten in radical form as:
[tex]\[
\sqrt[5]{\left(32 a^{10} b^{\frac{5}{2}}\right)^2}
\][/tex]
Thus, the correct answer is:
A. [tex]\(\sqrt[5]{\left(32 a^{10} b^{\frac{5}{2}}\right)^2}\)[/tex]
