S1 Math: Find p, q, ...

Question 1

p and q are both prime numbers. 
Find the values of p and q such that  is an integer.

Question 2

One third of the product of 68 and 108 is the same as 2^p x 3^q x 17^r

Find p, q, and r.

Question 3
Find smallest positive integer k  for   be a perfect cube

Solution:

Answer

(1) p = 11, q = 3

(2) p = 4, q = 2, r = 1

(3) k = (2 x 11)² = 484