if xy = 1, what is the value of \small \frac{2^{(x+y)^{2}}}{2^{(x-y)^{2}}}?

Question

Guys if xy = 1, what is the value of 2^(x + y)^2/2^(x-y)^2?  
    
A. 2  
B. 4  
C. 8  
D. 16  
E. 32  
    
Anyone preparing for GRE? #GRE #GREprep

Vijaya Lakshmi K · Answer

Hello Shubhankar,

The answer is option D.
The fraction would turn out to be 2 power (x+y)^2 divided by 2 power (x-y)^2. As the bases are the same, you can subtract the denominator power from the numerator when you write them as a single term. 
This would make your question be 2 power (((x+y)^2)-((x-y)^2))).
Now expand the power using basic (a+b)^2 and (a-b)^2. After subtraction, you will be left with the term 4xy in the power, which makes the expression to be 2^4xy.
Given xy=1, substitute it to get 2^4 which is 16.

Hope this helps. All the best.

if xy = 1, what is the value of \small \frac{2^{(x+y)^{2}}}{2^{(x-y)^{2}}}?

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