To the power of n/2 - how to get rid of it.

Question

In short, I have a formula $ \frac{2}{3}((-2)^{\frac{n}{2}}-1) $

I need to get rid of (n/2). I have to make sure that I only raise the number with degree n, the integer part, not n/2. Any ideas?

Replace $-2$ with $(i\sqrt{2})^2$. – David P Mar 03 '15 at 08:54 — David P, Mar 03 '15 at 08:54
Yeah, but I need to raise (-2) to the power of n. – user220631 Mar 03 '15 at 08:55 — user220631, Mar 03 '15 at 08:55

score 2 · Answer 1 · answered Mar 03 '15 at 09:03

2

$$(-2)^{\frac{n}{2}}=(-2)^{\frac{1}{2}n}=((-2)^{\frac{1}{2}})^n=(\sqrt{-2})^n=(\sqrt{-1}\cdot\sqrt{2})^n=(i\cdot\sqrt{2})^n$$

answered Mar 03 '15 at 09:03

barak manos

score 0 · Answer 2 · answered Mar 03 '15 at 10:06

0

$$\frac{2}{3}\left((-2)^{\frac{n}{2}}-1\right) = \frac{2}{3}\left(\sqrt{(-2)^n}-1\right)$$

answered Mar 03 '15 at 10:06

DanielV

2 Answers2