Answer the following questions related to rational exponents.

MATHEMATICS · Multi-part · GCSE · Mathematics · Number · Number

Problem

Answer the following questions related to rational exponents. (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. (ii) Write

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

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

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

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