Ta có:

a)  $2\sqrt{5}=\sqrt{2^{2}.5}=\sqrt{20}$

      $3\sqrt{2}=\sqrt{3^{2}.2}=\sqrt{18}$

Mà $\sqrt{18}<\sqrt{20}$

=> $2\sqrt{5}>3\sqrt{2}$ và $0<\frac{1}{3}<1

=> $(\frac{1}{3})^{2\sqrt{5}}<(\frac{1}{3})^{3\sqrt{2}}$.   ( đpcm)

b)  $6\sqrt{3}=\sqrt{6^{2}.3}=\sqrt{108}$

      $3\sqrt{6}=\sqrt{3^{2}.6}=\sqrt{54}$

Mà $\sqrt{54}<\sqrt{108}$

=> $3\sqrt{6}<6\sqrt{3}$

=> $7^{6\sqrt{3}}>7^{3\sqrt{6}}$.   ( đpcm)