Let and , where and…

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

Problem

Let

A = (\sqrt[5]{a^{3} b^{2}})^4 \cdot a^{1/2}

and

B = (a b^{3})^{2/5}

, where

a>0

and

b>0

. (i) Express

\sqrt[5]{a^{3} b^{2}}

as a power of

a

and a power of

b

using rational exponents. (ii) Find

A

in terms of

a

and

b

with rational exponents. (iii) Find

B

in terms of

a

and

b

with rational exponents. (iv) Hence simplify

\dfrac{A}{B}

, writing your answer with positive exponents only.