Please help

Nov 2009
149
21
Which is true?
(1) \(\displaystyle x^n\le |x^n|\)
(2) \(\displaystyle x^n\le |x|^n\)
Please justify
 
Jun 2013
1,127
601
Lebanon
assume that \(\displaystyle x\) is a real number and \(\displaystyle n \) is a natural number ?
 
Nov 2009
149
21
Yes. \(\displaystyle x\) is real and \(\displaystyle n\) is natural
 

Plato

MHF Helper
Aug 2006
22,490
8,653
Which is true?
(1) \(\displaystyle x^n\le |x^n|\)
(2) \(\displaystyle x^n\le |x|^n\)
Please justify
\(\displaystyle \forall n\in\mathbb{N}^+\left[|x^n|=|x|^n\right]\)