SOLUTION: simplify each number 64^3.5

Question 725451: simplify each number
64^3.5
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
First let's write the exponent as a fraction:

In general a fractional exponent can be written in radical form in two ways:

So we can rewrite as

(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.

Since the square root of 64 is 8 this becomes:

I'll leave it up to you to multiply this out.
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