Mathematics

Problem

Answer the following questions about rational exponents. a. (i) State the meaning of

a^{1/n}

for a positive real number

a

and an integer

n>1

. b. (ii) Show that

(\sqrt[n]{a})^{m}=a^{m/n}

for positive real

a

and integers

m,n>1

. c. (iii) Using the result in part (ii), write each of the following in rational-exponent form and evaluate: (a)

\sqrt[5]{32}

(b)

\sqrt[4]{81}