[tex] a^{2} + b^{2}-6a+4b+13=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ ( a^{2} -6a+9)+( b^{2} +4b+4)=0\ \textless \ =\ \textgreater \ \\ \ \textless \ =\ \textgreater \ ( a-3)^{2}+(b+2) ^{2} =0=\ \textgreater \ \\ \\ =\ \textgreater \ a-3=0=\ \textgreater \ a=3 \\ =\ \textgreater \ b+2=0=\ \textgreater \ b=-2[/tex]
[tex](3a+5b) ^{2014} =[3*3+5*(-2)] ^{2014}=(9-10) ^{2014}=( -1) ^{2014}=1. [/tex]
