Writing without negative exponent can someone please describe to me the method behind writing numbers without negative exponents such as:

Maybe just show me the logic / process? Especially for number (c) because fractions really confuse me.
Thanks in advance
 A: A.
\[
x^{-3}=\frac{1}{x^{3}}
\]
B.
\[
(2a+5)^{-1}=\frac{1}{2a+5}
\]
C.
\[
\left(\frac{a}{b}\right)^{-5}=\frac{1}{\left(\frac{a}{b}\right)^{5}}=\frac{1}{\left(\frac{a^{5}}{b^{5}}\right)}=\frac{b^{5}}{a^{5}}
\]
In general 
\[
x^{-a}=\frac{1}{x^{a}}
\]
And for fractions 
\[
\left(\frac{a}{b}\right)^{-c}= \left(\frac{b}{a}\right)^{c}=\frac{b^{c}}{a^{c}}
\]
A: Rule: $\left ( \frac{a}{b} \right)^m=\frac{a^m}{b^m}$
Applying this rule to our problem gives us $\left (\frac{a}{b} \right )^{-5}=\frac{a^{-5}}{b^{-5}}$
Rule: $ a^{-n}=\frac{1}{a^n}$
Applying this rule gives us $ \frac{a^{-5}}{b^{-5}}=\Large\frac{\frac{1}{a^5}}{\frac{1}{b^5}}=\frac{1}{a^5}\times \frac{b^5}{1}=\frac{b^5}{a^5}$
If you change the order in which we have applied the two rules, still we will get the same end result.
This link might be helpful:http://www.mathsisfun.com/algebra/exponent-laws.html
A: $$k^{-1}=\frac{1}{k}, k\neq 0$$
So:
$$ \left ( \frac{a}{b} \right )^{-5}=\left ( \left ( \frac{a}{b} \right )^{-1} \right )^5=\left (\frac{b}{a} \right )^5=\frac{b^5}{a^5}, a \neq 0$$
