For a non-zero x and y, and integers a and b, prove the following inequalities:
(1) x^(a+b) = x^a * x^b
(2) (xy)^a = x^a * y^a
can anyone give me a hint on how to prove these equalities
Try using logarithms. Here is a quick refresher: http://en.wikipedia.org/wiki/Logarithm.
I hope that's sufficient.
Using logarithms seems to me to be overkill here. If a and b are positive integers, then x^(a+b) means x multiplied by itself a+ b times. But, using the associative law to move parentheses, that is the same as x multiplied by itself a times and x multiplied by itself b times: x^ax^b.
Similarly, (xy)^a means xy multiplied by itself a times. Use the commutative law to write that as x multiplied by itself a times and y multiplied by itself a times: x^ay^a.
For a or b positive, use the fact that x^0= 1.
For a or b negative, use the fact that x^(-a)= 1/x^(a).