Question

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

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

Answer 1

Answer: (C)

$0$

We know that,

$a^m.a^n=a^{m+n}$
That is,

$mn=m+n.$
Now,

$m(n-2)+n(m-2)=mn-2m+nm-2n=2mn-2(m+n)=2(m+n)-2(m+n)=0$
$\therefore$ The required answer is $0$.