Can you please look into the question -

Does it mean \(n = P^{2Q}\)

or \(n = {P^2}Q\)
_________________

I have made the modification it is the second one.

Answer and explanation please.

N is a multiple of 5 so either P or Q or both have to be 5.

We are looking for a multiple of 25 so,

Among the given option the right ans should be a multiple of 25 and not simply be 5, 10 or 15 or other multiples of 5 but not a multiple of 25.

Lets start with A:

It could be that P^2 = 2^2 and Q = 5. Since this would result in N becoming a multiple of 5 but not a multiple of 25 option A is wrong
For option B
we can reverse the scenario such that P = 5 and Q =2; Yet this will be a multiple of 5 but not a multiple of 25

For option C
If we take the same two value 5 and 2 we get PQ = 10 and yet this will not be a multiple of 25

For option D

If anyone of P and Q is 5 this will be a multiple of 5 because both P and Q are squared hence 5^2 = 25 and this will be divisible by 25.
_________________

we are given that n is multiple of 5. n= p^2*Q where p and q are prime number
and asking which must be multiple of 25?
ok to make P or Q multiple of 25, one of them at least should equal to 25.
Similarly, n have to have at least one value of 5 to be multiple of 5.

(A) P^2 "can not be" why? ==> P could = 2 and q= 5 and hence 4 is not multiple of 25.
(B) Q^2 alone "can not be" for the same reason above.
(C) PQ still can not be. they could be 7*5 or 2*5 or even 5*5. and still we are not sure about the values of P and Q
(D) P^2*Q^2. This is the answer. if you apply the above, we will be getting 25 each time. which results in multiple of 25.
(E) p^3 q. can't be either.
_________________