If the problem is 2.3436 x 10^60, then there are 5 significant digits, each of the digits of 2.3436 is significant; count the number of significant digits in the number, not in the exponent.
If the problem is 2.3436 x 60, then there is only 1 significant digit. The number with the fewest number of significant digits wins and 60 has only 1 significant digit because zeros at the end of a number do not count, unless you are specifically told that they do.
If the problem is 2.3436 x 10^60, then there are 5 significant digits, each of the digits of 2.3436 is significant; count the number of significant digits in the number, not in the exponent.
If the problem is 2.3436 x 60, then there is only 1 significant digit. The number with the fewest number of significant digits wins and 60 has only 1 significant digit because zeros at the end of a number do not count, unless you are specifically told that they do.