a)
(5^{\sqrt3})^{\sqrt3}=5^{\sqrt3*\sqrt3}=5^3=125
b)
(3^{\sqrt2})^{2\sqrt2}=3^{\sqrt2*2\sqrt2}=2^{2*(\sqrt2)^2}=2^{2*2}=2^4=16
c)
(5^{\sqrt3-1})^{\sqrt3+1}=5^{(\sqrt3-1)(\sqrt3+1)}=5^{(\sqrt3)^2-1^2}=5^{3-1}=5^2=25
d)
(2^{\sqrt7-\sqrt2})^{\sqrt7+\sqrt2}=2^{(\sqrt7-\sqrt2)(\sqrt7+\sqrt2)}=2^{(\sqrt7)^2-(\sqrt2)^2}=2^{7-2}=2^5=32
e)
7^{\sqrt2}*49^{-\frac{\sqrt2}{2}}=7^{\sqrt2}*(7^2)^{-\frac{\sqrt2}{2}}=7^{\sqrt2}*7^{-\sqrt2}=7^{\sqrt2+(-\sqrt2)}=7^0=1
f)
9^{\sqrt5}*3^{1-2\sqrt5}=(3^2)^{\sqrt5}*3^{1-2\sqrt5}=3^{2\sqrt5+1-2\sqrt5}=3^1=3
g)
\frac{2^{\sqrt3+6}}{2^{\sqrt3+1}}=2^{\sqrt3+6-(\sqrt3+1)}=2^{\sqrt3+6-\sqrt3-1}=2^5=32
h)
\frac{6^{\sqrt3+1}*2^{-\sqrt3}}{3^{\sqrt3}}=\frac{3^{\sqrt3+1}*2^{\sqrt3+1}*2^{-\sqrt3}}{3^{\sqrt3}}=3^{\sqrt3+1-\sqrt3}*2^{\sqrt3+1+(-\sqrt3)}=
=3^1*2^{\sqrt3+1-\sqrt3}=3*2^1=3*2=6