Simplification

**Lisa87654** · February 28th 2008, 06:17 PM

Hi!

Can the following function be simplified any further?

[(2^0.5)(N^-0.5)]/2

If the - wasn't around i know it would simplify to (1/2)(sqrt(2N)), but I forget if there is a rule for this...

Thanks!
Lisa

**Mathnasium** · February 28th 2008, 06:27 PM

You've got:

$\frac{2^\frac{1}{2}}{2 \times n^ \frac{1}{2}}$ right now (moving the negative exponent to the denominator and making it positive.)

$\frac{2^\frac{1}{2}}{2}$ simplifies to $\frac{1}{2^\frac{1}{2}}$ (by subtracting the exponents of powers with the same bases).

This gives, essentially, $\frac{1}{\sqrt{2n}}$ .

**Lisa87654** · February 28th 2008, 06:36 PM

I guess I had forgotten (or quite possibly never knew) that N^(-0.5) was the same thing as 1/(N^0.5).
Thanks for your help!

**Mathnasium** · February 28th 2008, 06:42 PM

Yes, negative exponents can be made positive simply by moving them to the other half of the fraction.

$4^{-2} = \frac{1}{4^2}$

and

$\frac{1}{4^{-2}} = 4^2$ .

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