Question

What does it mean to raise a vector to the power -2/5? Example below.

Answer 1

I randomly ended up reading the following thread: http://openstudy.com/users/neemo#/updates/5025dd96e4b07eea166b1db7

The answer and an explanation is given at the bottom.

On the surface, I expected to at least understand the problem, as I'm familiar with linear algebra. However, after reading the thread and the answer a couple of times. I still don't understand parts of the question.

In particular, what do the following lines mean?

\[\left\{ \alpha, \beta, \gamma \right\} = \left\{ 1/6, 1/3\sqrt2,1/2\sqrt3 \right\}\]

\[\left\{ \alpha, \beta, \gamma \right\}^{(-2/5)} = 6\] How does one take the exponential power of a vector? As far as I knew, this is not even possible.

Answer 2

It's not \(\{\alpha,\beta,\gamma\}^{-\frac{2}{5}}\), it's \((\alpha\beta\gamma)^{-\frac{2}{5}}\).

Answer 3

Oh my, I feel silly now. Thank you.