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Ответ:

Применяем свойства степеней:

[tex]\boldsymbol{(a^{n})^{k}=a^{nk}\ ;\ \ a^{n}\cdot a^{k}=a^{n+k}\ ;\ \ a^{n}:a^{k}=a^{n-k}\ ;\ \ \sqrt[n]{\bf a^{k}}=a^{^{\frac{k}{n}}}\ ,\ a > 0}[/tex]   .  

[tex]\boldsymbol{2)\ \ \Big(a^{\sqrt6}\Big)^{\sqrt6}\cdot \Big(a^{\sqrt{3}+1}:a^{\sqrt3}\Big)=a^{\sqrt6\cdot \sqrt6}\cdot \Big(a^{\sqrt{3}+1-\sqrt3}\Big)}=\\\\\bf =a^6\cdot a^1=a^7[/tex]  

[tex]\boldsymbol{4)\ \ b^{^{\sqrt5}}\cdot b^{^{1,4}}\, :\, \sqrt[4]{b^{^{4\sqrt5}}}}=\bf b^{^{\sqrt5+1,4}}\, :\, b^{^{\sqrt5}}=b^{^{\sqrt5+1,4-\sqrt5}}=b^{1,4}=b^{\frac{7}{5}}}=}\sqrt[5]{\bf b^7}[/tex]