Consider the expression for a positive real number and integers with .

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

Consider the expression

a^{\tfrac{m}{n}}

for a positive real number

a

and integers

m,\,n

with

n>0

. (i) Explain how

a^{\tfrac{m}{n}}

can be interpreted by using the concept of the

n

th root of a number. (ii) Using the explanation from part (i), show that

(27)^{\tfrac{2}{3}}=9