Mathematics

Problem

Answer the following questions related to rational exponents and radicals. a. (i) State the relationship between

a^{\frac{1}{n}}

and

\sqrt[n]{a}

for

a>0

and

n\in\mathbb{N}

. b. (ii) Using the relationship stated in part (i), show that

81^{\frac{1}{4}} = 3

. c. (iii) Explain why

(\sqrt[3]{8})^{2} = 8^{\frac{2}{3}}