Correct answer: (D)
Solution: While this problem appears to be a typical exponent problem that you manipulate algebraically, it is best solved with basic arithmetic concepts. On the left side, 36/3^4 can be reduced to 4/9 so that the original equation now reads 4/9=1/3^m +1/3^n Using logic and an understanding of fractions, you can now deduce the values of m and n. Neither n nor m could be 0 or negative as that would make one of the terms on the right greater than or equal to 1 and the sum could never equal the fraction 4/9. Since the lowest common denominator has to be nine, consider the different positive values that add to 4/9. The only possibilities are 1/9+ 3/9 or 2/9+ 2/9. Only the first can be written with 1s in the numerator and 3s in the denominator. 1/9+3/(9 ) can be expressed in 3rds as 1/9+1/3, or 1/3^2 +1/3^1 . Therefore it must be true that either m = 2 and n = 1, or n = 1 and m = 2. Since they are asking for the sum, it does not matter which is which. The answer is 2 +1, or 3.
