Undergrad Simplifying this absolute value

[Mr Davis 97]

I have the expression $|nr^n|^{1/n}$. A quick question is whether I can allow the exponent to go inside of the absolute value. I know that if it were an positive integral exponent then because of the multiplicativity of the absolute value function that would be allowed. But I'm not sure what I'm allowed to do in the case of this rational exponent...

 

[mfb]

In the real numbers that works.

 

[Stephen Tashi]

whether I can allow the exponent to go inside of the absolute value.

Are you asking whether $|n r^n|^{1/n} = | (n r^n)^{1/n}|$ ?

Try $r = 1,\ n = -2$.

 

[Mr Davis 97]

Are you asking whether $|n r^n|^{1/n} = | (n r^n)^{1/n}|$ ?

Try $r = 1,\ n = -2$.

So it's not generally true then? What if $n$ is positive?

 

[mathman]

If n and r are both positive then absolute value can be ignored.

 

[Mr Davis 97]

If n and r are both positive then absolute value can be ignored.

Well $n$ is positive while $r$ is not necessarily positive.