Having problems with Exponents $1^n =1$ where n is a positive integer I understand.
But $1^{1/2}$ or $1^{0.5}$ is also $1$, I have difficulty in understanding that.
And does that mean $1^n$ where n is any positive real no equals $1$?
$2^{-5}$ = $1 / 2^5$ = $1/32 =0.03125 $
I can compute this but I really don't understand this law.How can you raise something to negative power and if you can how is it obtained by removing the $-$ sign and dividing it by $1$ ?                                          

$1^N = 1$ for any real value of N.
You are OK with the case of N being integer. This is good start.
The case where $N$ is not integer, as in your example: $1^{0.5}$ (also referred to as $\sqrt{1}$) could be justified as follows:
What is the number $x$ that if you multiply it by itself, you get 1?
This calls for solving the equation $$x^2=1$$ Taking the square root of both sides, we get two numbers that satisfy the equation, namely the number $+1$ and the number $-1$. 
That is for the $+1$ case: $$\sqrt{x^2}=\sqrt{1}=1^{0.5}=1$$
I hope that his is somewhat convincing.
As for the negative powers part, think of how you would do $\frac{4^3}{4^5}$, you may want to write it down as where the "." is a multiplication sign:
$$K=\frac{4^3}{4^5} = \frac{4.4.4}{4.4.4.4.4}=\frac{1}{4.4}$$
If you notice the powers of the numerator (3) and the denominator (5) and compare them with the power of the denominator (2), you may observe that $5-3=2$. That is we could write:
$$K=\frac{4^3}{4^5}=\frac{1}{4^{5-3}}=\frac{1}{4^{2}}$$
Suppose now we want to calculate $Z$ by multiplying $K$ by $4^7$:
$$Z=4^{7}\frac{1}{4^{2}}$$
Using the above approach:
$$Z=4^{7}\frac{1}{4^{2}}=\frac{4.4.4.4.4.4.4}{4.4}=4.4.4.4.4=4^5$$
Observe the powers here:
$$Z=4^{7}\frac{1}{4^{2}}=4^5$$
Do you see that $7-2=7+(-2)=5$?
The (-2) here is what you use the negative power for.
That is why we can do:
$$Z=4^{7}.4^{-2}=4^{7-2}=4^5$$
and we can do $$K=\frac{4^3}{4^5}=4^{3-5}=4^{-2}=\frac{1}{4^2}$$
This may be a good read: What do Fractional Exponents mean
