Indices and Surds

If m & n are positive integers, then

(a^m)*(a^n) = a^(m+n)
(a^m)/(a^n) = a^(m-n), when a is not 0.
(ab)^n = (a^n)*(b^n)
(a^m)^n = a^(m*n)
(a/b)^n = (a^n)/(b^n), when b is not 0.
A^0 = 1, when a is not 0.

If a^x=k, then a=k^(1/x), when x is not 0.
If a^ (1/x)=k, then a=k^x, when x is not 0.
If a^x=b^y, then a=b^(y/x) and b=a^(x/y), when x, y is not 0.
If a^x=a^y, then x=y, when a is not 0 or 1.
a^(-n)=1/(a^n)
a^(b^c) is not equal to (a^b)^c, when b is not equal to c.