Question 996847
this is clearer if it's written than if it's typed, so .....


<img src = "http://theo.x10hosting.com/2015/101504.jpg" alt="$$$" </>


i checked this by making m = 5 and n  = 3 and evaluating the original expression and the final expression to see if they came up with the same answer.


they did which confirmed the solution was good.


basic concepts involved are:


(a^b)^c = a^(b*c)


(a^b * c^d)^e = a^(b*e) * c^(d*e)


for example:


(2^3)^2 = 2^(3*2) = 2^6
(2^3)^2 = 64 (original expression)
2^6 = 64 (final expression)


(2^3*3^4)^2 = 2^(3*2) * 3^(4*2) = 2^6 * 3^8
(2^3*3^4)^2 = 419904 (original expression)
2^^ * 3^8 = 419904 (final expression)


also:


a^b / a^c = a^(b-c)


for example:


2^5 / 2^3 = 2^(5-3) = 2^2
2^5 / 2^3 = 4 (original expression)
2^2 = 4 (final expression


here's a reference that should be helpful if you wish to take the time to read it.


<a href = "http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm" target = "_blank">http://www.wtamu.edu/academic/anns/mps/math/mathlab/beg_algebra/beg_alg_tut26_exp.htm</a>