I'm wondering if there is a way to add two numbers with the same base but different exponents without converting the base of the numbers. For example lets say your adding 2^2 and 2^4 the value of 2^2 is 4 and the value of 2^4 is 16 so the total of the two numbers is 20. The closest I could get my calculator to finding a base of 2 with a value of 20 was 2^4.3219281 which equaled 20.000000071. So I have a few questions.
Can 2 be raised to a power that's exactly equal to 20?
I know that with division and multiplication you can just add or subtract the exponents. Are there any similar tricks for adding or subtracting values with exponents?
Is there anyway to arrive at the result, or a similar result of 2^4.3219281 without changing the base in the process?