Question

If $a^m{a}^n=a^{mn}$, then $m(n-2)+n(m-2)$ is equal to

• A. $-1$
• B. $+1$
• C. $0$
• D. $-\frac{1}{2}$

Answer 1

The correct option is C $0$

Given $a^m{a}^n=a^{mn}\Rightarrow a^{m+n}=a^{mn}$

$\therefore m+n=mn$ .....(i)

$m(n-2)+n(m-2)=2mn-2(m+n)$

$=2[mn-m-n]$

By using (i)

$=0$