Question

HHHEEEELLLPPPPPP!!

This is such a simple question but I am not getting it! -_-"

Proof the given attachment !

Gracias!​

Answer 1

Well,

$\begin {aligned}&\textsf{LHS}\\\\\implies\ \ &a^m\div a^n\\\\\implies\ \ &\dfrac {a^m}{a^n}\\\\\implies\ \ &\dfrac{\overbrace{a\times a\times a\times\dots\times a}^{m}}{\underbrace{a\times a\times a\times\dots\times a}_{n}}\end{aligned}$

Let $m>n,$ so,

$\begin{aligned}\implies\ \ &\dfrac{\overbrace{a\times a\times a\times\dots\times a}^{m-n+n}}{\underbrace{a\times a\times a\times\dots\times a}_{n}}\\\\\implies\ \ &\dfrac{\overbrace{a\times a\times a\times\dots\times a}^{m-n}\times\overbrace{a\times a\times a\times\dots\times a}^{n}}{\underbrace{a\times a\times a\times\dots\times a}_{n}}\end {aligned}$

$\begin {aligned}\implies\ \ &\underbrace{a\times a\times a\times\dots\times a}_{m-n}\\\\\implies\ \ &a^{m-n}\\\\\implies\ \ &\textsf {RHS}\end {aligned}$