Question

Prove that :-
${\left(\frac{n^m}{n^n}\right)}^l\times {\left(\frac{n^n}{n^l}\right)}^m\times {\left(\frac{n^l}{n^m}\right)}^2=1$

Answer 1

${\left(\frac{n^m}{n^m}\right)}^l\times {\left(\frac{n^n}{n^l}\right)}^m\times {\left(\frac{n^l}{n^m}\right)}^n=1$

$\Rightarrow \frac{n^{ml}}{n^{nl}}\times \frac{n^{nm}}{n^{lm}}\times \frac{n^{ln}}{n^{mn}}$

$n^{ml+nm+ln-nl-lm-mn}$

$\Rightarrow n$

$\Rightarrow n^0=1$.

Hence proved.