[tex]\it 2^{30^2} =2^{900};\ \ (32^4)^{100} =32^{400} =(2^5)^{400}=2^{2000}
\\\;\\
x = (2^{900}\cdot2^{600}+2^{2000}:2^{500})\cdot 2 = (2^{1500}+2^{1500})\cdot2 =
\\\;\\
=2\cdot2^{1500}\cdot2 = 2^{1+1500+1} = 2^{1502} = (2^{751})^2[/tex]
_______________________________
[tex]\it 9^{1000} = (3^2)^{1000} = 3^{2000}
\\\;\\
y = 5\cdot(3^{2002} - 3^{2001}-3^{2000}) = 5\cdot3^{2000}(3^2-3-1)=
\\\;\\
=5\cdot(3^{1000})^2\cdot5 = 5^2\cdot(3^{1000})^2 = (5\cdot3^{1000})^2
[/tex]
