\(\frac{3^{-(x+y)}}{3^{-(x-y)}}=?\)
Let's simplify the above equation:
= \(\frac{3^{(x-y)}}{3^{(x+y)}}\)
= \(\frac{3^x * 3^-y}{3^x * 3^y}\)
Cancel out \(3^x\)
\(= \frac{3^-y}{3^y}\)
\(= 3^-2y = ?\)
\(= \frac{1}{3^2y} = ?\)
As per above if we know the value of y we should be able to find the answer.
\(1) x=3\)
Clearly not sufficient as we are not aware of the value of x
Hence, (1) =====> is NOT SUFFICIENT\(2) y=2\)
As we know the value of y now, we can plug this value in the above equation
\(= \frac{1}{3^2y}\)
\(= \frac{1}{3^2*2} = \frac{1}{3^4} = \frac{1}{81}\)
As we are able to determine the value, B is sufficient
Hence, (2) =====> is SUFFICIENTHence, Answer is B
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