Question

If $a^m.a^n=a^{mn}$ then find the value of $m(n-2)+n(m-2)$

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is A $0$

Given $a^m.a^n=a^{mn}$
$\Rightarrow a^{m+n}=a^{mn}\Rightarrow m+n=mn$
Now $m(n-2)+n(m-2)=mn-2m+nm-2n$
$=2mn-2(m+n)=2mn-2mn=0$