brain teaser

given that 2^x = 1/square root of 2 and 2^y = 4(square of 2), find exact values of x and y.
calculate the exact value of 2^y-x

thanks..

Ok... because sqrt(n) = n^(1/2) and 1/(n^p) = n^(-p)
2^x = sqrt(2)^(-1) = 2^(-1/2)
so x = 1/2
2^y=2^2=4
so y = 2

2^(x-y) = 2^(2-1/2) = 2^(3/2)
and since n^(3/2) = sqrt(n^3), the final answer is sqrt(8) which is the same as 2*sqrt(2)

2^x = 1/sqrt(2)
2^x = 1/ [2^(1/2)]
2^x = 2^(-1/2)
x = -1/2 or -0.5 -----------answer.

2^y = 4sqrt(2)
2^y = (2^2)[2^(1/2)]
2^y = 2^(2 +1/2))
2^y = 2^(5/2)
y = 5/2 or 2.5 -----------answer.

2^(y -x)
= 2^(2.5 -(-0.5))
= 2^(3.0)
= 8 ---------------answer.

Argh... stupid negatives :mad:
Bah...