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

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- Feb 21st 2010, 04:28 PMharish21Equalities
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 - Feb 21st 2010, 05:37 PMsimulacrumLogs
Try using logarithms. Here is a quick refresher: http://en.wikipedia.org/wiki/Logarithm.

I hope that's sufficient. - Feb 21st 2010, 05:54 PMharish21
- Feb 22nd 2010, 03:21 AMHallsofIvy
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).