Rational terms in a Binomial expansion

Question

Find the number of rational terms in the expansion of (9^1/4 + 4^1/6)¹⁰⁰

A- 101

B- 100

C- 51

D- 17

Answer 1

If you expand the given expression you will have

(9^(1/4) + 4^(1/6))^100=∑_k=0¹⁰⁰ (_k¹⁰⁰)*3⁵⁰*[2^(1/3)/3^(1./2)]^k.

 

Can you find out now for which k's [2^(1/3)/3^(1./2)]^k is (not) rational?