Explanation:

3⁹⁰ + 5⁹⁰ can be written as (3²)⁴⁵ + (5²)⁴⁵
= (9)⁴⁵ + (25)⁴⁵

Any number of the form aⁿ + bⁿ is a multiple of (a + b) whenever n is odd.

So (9)⁴⁵ + (25)⁴⁵ is a multiple of 9 + 25 = 34

So, the remainder when we divide (3²)⁴⁵ + (5²)⁴⁵ by 34 is equal to 0.

The question is "What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?"

Hence the answer is "0".

Choice A is the correct answer.