AbdurRakib wrote:

If x and y are distinct prime numbers, which of the following could be true?

A. \(\frac{x^y}{y}\) is an odd integer

B. \(x^2y^3\)=\(x^2\)

C. \(\frac{y^x}{4}\) is an even integer

D. \(\frac{xy}{2}\) is an even integer

E. \(x^y\)=\(y^x\)

Given, x and y are distinct Prime numbers.

A. \(\frac{x^y}{y}\) is an odd integer --> x and y doesn't have anything in common. So, the division would never be an Integer.Incorrect

B. \(x^2y^3\)=\(x^2\) --> it means y is 1 but i is not a prime number. Incorrect

C. \(\frac{y^x}{4}\) is an even integer --> For y=2 and X=3, we will have 8/4=2. An even Integer. Hence Correct Answer

D. \(\frac{xy}{2}\) is an even integer --> if xy/2 is integer, then one of x or y must be 2. which would mean it will cancel with the 2 at the denominator , hence it can never be Even. Incorrect

E. \(x^y\)=\(y^x\)[/quote] for two distinct primes, this property will never be true. Check for any set of pair. Incorrect

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