Not a real number

bkbowser · #1 $Old$ November 2nd, 2009, 12:55 PM

$(-1/36)^-1/4$ 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.
$(-1/36)^-1/4$ 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 $-(36^1/4)$ and $-(1^1/4)$ .
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?

tonio · #2 $Old$ November 2nd, 2009, 01:41 PM

Quote:

Originally Posted by bkbowser $View Post$

$(-1/36)^-1/4$ 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.
$(-1/36)^-1/4$ 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 $-(36^1/4)$ and $-(1^1/4)$ .
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):

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

Tonio