a)
(5^{\sqrt2})^{\sqrt2}=5^{\sqrt2*\sqrt2}=5^2=25
b)
4^{\sqrt3}*4^{2-\sqrt3}=4^{\sqrt3+2-\sqrt3}=4^2=16
c)
(2^{\sqrt6})^{\sqrt6}=2^{\sqrt6*\sqrt6}=2^6=64
d)
5^{2+\sqrt5}*5^{2-\sqrt5}=5^{2+\sqrt5+2-\sqrt5}=5^{4}=625
e)
3^{\sqrt{27}}:3^{3\sqrt3}=3^{3\sqrt3}:3^{3\sqrt3}=3^{3\sqrt3-3\sqrt3}=3^0=1
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\sqrt{27}=\sqrt{9*3}=3\sqrt3
f)
7^{4+2\sqrt2}:7^{2+\sqrt8}=7^{4+2\sqrt2-(2+2\sqrt2)}=7^{4+2\sqrt2-2-2\sqrt2}=7^2=49
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\sqrt8=\sqrt{4*2}=2\sqrt2