a proof for a probably common problem?

Question

Can someone provide a proof for the following problem? I know that this might be a common proof to some common problem that I am yet to know, and that if someone would leave a proof it would give me a deeper understanding of powers.

$$x^{-n}=\frac {x}{x^{(n+1)}}$$

Multiply both sideds with $x^{n+1}$ (of course assuming taht $x\ne 0$, which must be assumed anyway)? — Hagen von Eitzen, Oct 30 '14 at 18:17

score 0 · Answer 1 · answered Oct 30 '14 at 18:26

0

Notice that $x^{n+1}= x\cdot x^n$ and $x^{-n} = \frac 1n$ so: $$x^{-n}=\frac{x}{x \cdot x^n} \rightarrow \frac{1}{x^n}=\frac{1}{x^n}$$

answered Oct 30 '14 at 18:26

PunkZebra

1,595

You're welcome and remember to +1 and accept! – PunkZebra Oct 31 '14 at 17:59

a proof for a probably common problem?

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