Mathematics

Problem

Let

x>0

. Consider the nested radical

\sqrt{\sqrt[3]{x^{6}}}

. a. (i) Rewrite

\sqrt{\sqrt[3]{x^{6}}}

as a single power of

x

with a rational exponent. b. (ii) Simplify the exponent obtained in part (i). c. (iii) If

x=\sqrt[5]{32}

, evaluate the simplified expression and express the answer as a rational number.