[tex]log_{4}( \frac{a^{4}b}{16} )^{ \frac{1}{5} } = \frac{1}{5}*(log_{4} a^{4}b-log_{4}16)=
\frac{1}{5} *(log_{4}a^{4}+log_{4}b-log_{4}4^{2})=
[/tex]
[tex]= \frac{1}{5} *(4log_{4}a+log_{4}b -2log_{4}4)= \frac{4}{5} log_{4}a+ \frac{1}{5} log_{4}b- \frac{2}{5} [/tex]
