SOLUTION: simplify each number 64^3.5

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Question 725451: simplify each number
64^3.5
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
First let's write the exponent as a fraction:
64%5E%28%287%2F2%29%29
In general a fractional exponent can be written in radical form in two ways:
a%5E%28%28m%2Fn%29%29+=+root%28n%2C+a%5Em%29+=+%28root%28n%2C+a%29%29%5Em
So we can rewrite 64%5E%28%287%2F2%29%29 as
root%282%2C+64%5E7%29
or
%28root%282%2C+64%29%29%5E7
(Note: These are square roots. We often don't bother writing the 2 because if there is no number in that position that it is assumed that it is a 2.)

Now we have to ask ourselves, which looks easier? The first one where we raise 64 to the 7th power and then find a square root? Or the second one where we find the square root of 64 and then raise that to the 7th power. I think you'll agree that since the square root of 64 is a well-known whole number, the second one is easier.
%28root%282%2C+64%29%29%5E7
Since the square root of 64 is 8 this becomes:
8%5E7
I'll leave it up to you to multiply this out.