What is 2 to the power of 647 divided by 5 + 6437?

Question

It was on my homework.

Answer 1

What is divided by 5? the power or 2 raised to the power?

2^(647/5) or (2^647)/5

is it: divided by 5, then add 6437 to the result?
or ; divided by (5+6437)?

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There are 4 possible calculations.

One possibility:
2^(647/5) + 6437

2^(645/5)*2^(2/5) + 6437

(2^129)*4^(1/5) +6437

2^129 is a number that has 39 digits, beginning with 680,56... and finishing with a 6.

4^(1/5) is the fifth root of 4 = approx. 1.3195... with digits going on forever (it is an irrational number)

The product is a number of 39 digits before the decimal point, and a decimal portion that goes on forever.

Adding 6437 to the product will only change the last 4 or 5 digits before the decimal point. The final answer would be just below 9 x 10^38.

Because it does not make sense to worry about adding such a small number (6437) to such a large number (2^(647/5)), I suspect that it is not a correct interpretation of your problem.

Answer 2

A big-*** number, close to 200-digits long. You sure thiis is the problem from your homework?

Answer 3

I doubt it but anyhoo...assuming hierarchy of operations is followed...1.167*10^194