For which of the following values of n is \((-0.5)^n\) the greatest?

Remember, any value in decimal, when the power is applied its absolute value decreases.
for 0.5 > 0.5^2.
here, because of the negative sign, it gives the question another twist!
now a positive sign will always be greater than negative !!
negative to the power even nos will be positive right!
so here we have to check positive powers as greatest is required,
also with increasing power, the no will be getting smaller.
hence basically we are looking at the smallest even no in the options.
which is 2 which is also the ans.