Priya78240 wrote:

if x and y are integers ,what is the value of (2^x)^y

1. 2^x + 2^y = 9

2. x.y = 0

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First off, Welcome to GMATClub -

Priya78240Let's first set some basics straight - both a^0 1^a is always equal to 1

On analyzing the individual statements.

1. 2^x + 2^y = 9 Sum of two exponents whose base is even must be odd.

There is only one possibility for the base to be odd - when one of the two bases result

in an odd integer. The only possibility is when one of the even bases has 0 as a power,

making it the zero. If x = 0, \((2^x)^y\) will be 1^y which is 1. Also, if y = 0, the

expression \((2^x)^y\) will always yield a zero

(Sufficient)2. xy = 0This is possible when x,y, or both have a value of 0.

Whichever case we consider, the value of \((2^x)^y\) will be 0 without fail. This

makes the details of the individual statement enough

(Sufficient - Option D)
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