Evaluate and justify the value of a rational power:

MATHEMATICS · Multi-part · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Evaluate and justify the value of a rational power: (i) Rewrite

(64)^{2/3}

in the form

\sqrt[3]{(\; )}

(\; )^{1/3}

before simplifying. (ii) Calculate the exact numerical value of

(64)^{2/3}

. (iii) Using your answer, verify that

(a^{m/n})^{\;n}=a^{m}

for

a=64

m=2

, and

n=3

. State each step clearly.