Not a real number

• Nov 2nd 2009, 10:55 AM
bkbowser
Not a real number
$\displaystyle (-1/36)^-1/4$ The answer section is saying that this is not a real number. The -1/4 is an exponent.

First off I'd like to make sure I have the question correct.
$\displaystyle (-1/36)^-1/4$ is asking me for the quotient of one and the negative quotient of the fourth root's of 1 and 36. Which ends up as the quotient of$\displaystyle -(36^1/4)$ and $\displaystyle -(1^1/4)$.
Secondly, although i understand that this is not a real number, I am confused by the vague definition. If it isnt a real number what is it?
• Nov 2nd 2009, 11:41 AM
tonio
Quote:

Originally Posted by bkbowser
$\displaystyle (-1/36)^-1/4$ The answer section is saying that this is not a real number. The -1/4 is an exponent.

First off I'd like to make sure I have the question correct.
$\displaystyle (-1/36)^-1/4$ is asking me for the quotient of one and the negative quotient of the fourth root's of 1 and 36. Which ends up as the quotient of$\displaystyle -(36^1/4)$ and $\displaystyle -(1^1/4)$.
Secondly, although i understand that this is not a real number, I am confused by the vague definition. If it isnt a real number what is it?

It's a complex number, just like any other even root of any negative real number (but NOT only these, of course):

$\displaystyle \left(-\frac{1}{36}\right)^{-1/4}=\left(-36\right)^{1/4}=$$\displaystyle \sqrt[4] {-36}$$\displaystyle =\sqrt{-6}$

Tonio