a)
6^{1-\sqrt2}*6^{\sqrt2+1}=6^{1-\sqrt2+\sqrt2+1}=6^2=36
b)
5^{\pi+3}:5^{\pi}=5^{\pi+3-\pi}=5^3=125
c)
2^{3\sqrt5}*8^{-\sqrt5}=(2^3)^{\sqrt5}*8^{-\sqrt5}=8^{\sqrt5}*8^{-\sqrt5}=8^{\sqrt5+(-\sqrt5)}=8^0=1
d)
4^{\sqrt3}:2^{2\sqrt3}=4^{\sqrt3}:(2^2)^{\sqrt3}=4^{\sqrt3}:4^{\sqrt3}=4^0=1
e)
6^{\sqrt3}*3^{1-\sqrt3}*2^{-\sqrt3}=(3*2)^{\sqrt3}*3^{1-\sqrt3}*2^{-\sqrt3}=3^{\sqrt3}*2^{\sqrt3}*3^{1-\sqrt3}*2^{-\sqrt3}=3^{\sqrt3+1-\sqrt3}*2^{\sqrt3+(-\sqrt3)}=3^1*2^0=3*1=3
f)
4^{\pi+3}*3^{\pi}:12^{\pi}=\frac{4^{\pi+3}*3^{\pi}}{(4*3)^{\pi}}=\frac{4^{\pi+3}*3^{\pi}}{4^{\pi}*3^{\pi}}=4^{\pi+3-\pi}*3^{\pi-\pi}=4^3*3^0=64*1=64