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}=8^{\sqrt5+(-\sqrt5)}=8^{\sqrt5-\sqrt5}=8^0=1
d)
4^{\sqrt3}:2^{2\sqrt3}=\frac{2^{2\sqrt3}}{2^{2\sqrt3}}=2^{2\sqrt3-2\sqrt3}=2^0=1
e)
6^{\sqrt3}*3^{1-\sqrt3}*2^{-\sqrt3}=6^{\sqrt3}*3^{1-\sqrt3}*(\frac{1}{2})^{\sqrt3}=(6*\frac{1}{2})^{\sqrt3}*3^{1-\sqrt3}=3^{\sqrt3}*3^{1-\sqrt3}=3^{\sqrt3+1-\sqrt3}=3^1=3
f)
4^{\pi +3}*3^{\pi}:12^{\pi}=4^{\pi+3}*(\frac{3}{12})^{\pi}=4^{\pi+3}*(\frac{1}{4})^{\pi}=4^{\pi+3}*4^{-\pi}=4^{\pi+3+(-\pi)}=4^{\pi+3-\pi}=4^3=64