Which is true? (1) x^n\le |x^n| (2) x^n\le |x|^n Please justify

kjchauhan Nov 2009 149 21 Jan 7, 2020 #1 Which is true? (1) \(\displaystyle x^n\le |x^n|\) (2) \(\displaystyle x^n\le |x|^n\) Please justify

I Idea Jun 2013 1,127 601 Lebanon Jan 8, 2020 #2 assume that \(\displaystyle x\) is a real number and \(\displaystyle n \) is a natural number ?

kjchauhan Nov 2009 149 21 Jan 8, 2020 #3 Yes. \(\displaystyle x\) is real and \(\displaystyle n\) is natural

P Plato MHF Helper Aug 2006 22,490 8,653 Jan 8, 2020 #4 kjchauhan said: Which is true? (1) \(\displaystyle x^n\le |x^n|\) (2) \(\displaystyle x^n\le |x|^n\) Please justify Click to expand... \(\displaystyle \forall n\in\mathbb{N}^+\left[|x^n|=|x|^n\right]\)

kjchauhan said: Which is true? (1) \(\displaystyle x^n\le |x^n|\) (2) \(\displaystyle x^n\le |x|^n\) Please justify Click to expand... \(\displaystyle \forall n\in\mathbb{N}^+\left[|x^n|=|x|^n\right]\)