Data Sufficiency

What is the value of 3^-(x+y)/3^-(x-y)?

(1) x=2
(2) y=3

B

When you raise a number to a negative exponent, it is equivalent to taking the recirpocal of the number and raising it to the opposite of the negative exponent. In other words...

2^(-3) = 1/(2^3) = 1/8.

Using this, (3^-(x+y))/(3^-(x-y)) can be written as

(3^(x-y))/(3^(x+y))

When different powers of the same base are multiplied together, you can combine them and add the exponents. For example,

(3^5)*(3^7)*(3^3) = 3^(5+7+3) = 3^15.

Therefore,

(3^(x-y))/(3^(x+y)) = ((3^x)(3^-y))/((3^x)(3^y))

Then, the 3^x in the numerator and denominator cancel out and you are left with

(3^-y)/(3^y) = 1/((3^y)(3^y))

When expressed like this, it is clear that statement (1) will not help you b/c the x's cancel out. However, knowing the value of y will allow you to determine the value of the expression.