Simplifying this absolute value

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• Mr Davis 97

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...

In the real numbers that works.

Mr Davis 97
Mr Davis 97 said:
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##.

Stephen Tashi said:
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?

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

mathman said:
If n and r are both positive then absolute value can be ignored.
Well ##n## is positive while ##r## is not necessarily positive.