Mathematics

Problem

Answer the following questions related to rational exponents. a. (i) Define

a^{\frac{m}{n}}

for a positive real number

a

and positive integers

m

and

n

. State the meaning of the symbols used. b. (ii) Write

(32)^{\frac{3}{5}}

in radical form and evaluate its numerical value. c. (iii) Verify that

(\sqrt[5]{32})^{3}

gives the same result as obtained in part (ii) and explain why this is so.