Mathematics

Problem

Let

E = \dfrac{3a\sqrt[3]{2a^{2}}}{\sqrt[3]{4a^{5}}}

, where

a>0

. a. (i) Rewrite the denominator of

E

using rational exponents. b. (ii) Find the least expression under a cube root that must be multiplied to the numerator and the denominator so that the denominator becomes a rational number. c. (iii) Hence, rationalize the denominator of

E

and simplify the resulting expression, writing your final answer with positive integral exponents of

a

and no radical in the denominator.

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