If x is a non-zero integer, what is the value of x ^ y?

(1) x = 2
(2) (128 ^ x)[6 ^ (x + y)] = (48 ^ 2x)(3 ^ -x)


Official Answer and Explanation to the above problem

One of the most effective ways to begin solving problems involving exponential equations is to break down bases of the exponents into prime factors and combine exponents with the same base. Following this approach, be sure to simplify each statement as much as possible before arriving at the conclusion, since difficult problems with exponents often result in unobvious outcomes.

(1) INSUFFICIENT: While this statement gives us the value of x, we know nothing about y and cannot determine the value of x^y.

(2) SUFFICIENT: (128^x)[6^(x + y)] = (48^2x)(3^-x)

[(2^7)^x][(2 × 3)^(x + y)] = {(2^4 ) 3]^2x}(3^-x)

[(2^7)^x][2^(x + y)][3^(x + y)] = (2^8x)(3^2x)(3^-x)

[2^(8x + y)][3^(x + y)] = (2^8x)[3^(2x - x)]

(2^8x)( 2^y)(3^x)(3^y) = (2^8x)(3^x)

( 2^y)(3^y) = 1

(2 × 3)^y = 1

6^y = 1

y = 0

Since y = 0 and x is not equal to zero (as stated in the problem stem), this information is sufficient to conclude that x^y = x^0 = 1.

The correct answer is B.