Two fifths of a number is a perfect cube Which of the follow

Two fifths of a number is a perfect cube. Which of the following statements must be true? (Mark all that apply.) (a) The number cannot possibly have 3 fives in its prime factorization. (b) The number cannot possibly have 3 twos in its prime factorization. (c) The number cannot possibly have 4 fives in its prime factorization. (d) The number cannot possibly have 4 twos in its prime factorization.

Solution

a) True as 5 of the (2/5) will cancel out one of the 5 hence it wont be a perfect cube

b) True as 2 of the (2/5) will be multiplied with the 3 twos and hence it wont be a perfect cube

c) False as one of the 4 fives will be cancelled out by the (2/5) denominator which leaves 3 fives which could make the number a perfect cube

d) True as the 2 from (2/5) will be multiplied making it 5 twos hence the number cannot be a perfect cube