2 to the power of 3.5 (2e3.5) Is this a real algebra equation?

Question

I misinterpreted a simple equation, leading me to think of powers(exponents) that are not whole numbers. 2(2)(2)=8.
2(2)(2)(1)=8. So does the .5 mean nothing? Or mean nothing just in this case?

Answer 1

It means something.

For example you can write the square root of a number "a" as:

a^.5

.

Answer 2

The .5 DOES mean something. For example, 3^(.5) multiplied by itself is 3 (since when you multiply, the exponents add). Therefore 3^(.5) is the square root of 3.

So 2^(3.5) = (2^3)(2^(.5)) = 8(2^(.5)) = 8 times the square root of 2. This is probably what your problem is asking you to work out.

Answer 3

Sure it means something. An exponent of .5 is the same as a square root since a^n * a^n = a^(2n)

Were you in class when the teacher went over that?

Doug

Answer 4

when you have an exponent that is 1/2 it means the square root of the number

1/3 means the cubed root and so on