a,\(we\) \(have:\)\(516=516^n\div516^{13}=516^{n-13}\)

  \(but\)\(516=516^1.\) \(So\) \(that:\)  \(516^1=516^{n-13}.\) \(Inferred\): \(n-13=1.\)

\(so :n=14\)

b,\(3427^2=3427^6\div3427^n=3427^{6-n}.\) \(So\) \(that\)\(6-n=2\) \(or\) \(n=6-2.\) \(so : n=4\)

c,\(we\) \(know:\) \(64=8^2\) \(and\) \(8=8^1\) \(so\) \(8^2=64=8^n\div8^1=8^{n-1}.\)

\(so\) \(that:\) \(n-1=2.\) \(So\) \(n=3\)