已知数列\(\{a_{n}\}\)满足：\(a_{n+1}-a_{n}=d(n∈N^{*})\)，前\(n\)项和记为\(S_{n}\)，\(a_{1}=4\)，\(S_{3}=21\)．
\((1)\)求数列\(\{a\)\({\,\!}_{n}\)\(\}\)的通项公式；
\((2)\)设数列\(\{b\)\({\,\!}_{n}\)\(\}\)满足\(b\)\({\,\!}_{1}\)\(=\)\( \dfrac{16}{7}\)，\(b\)\({\,\!}_{n+1}\)\(-b\)\({\,\!}_{n}\)\(=2^{a_{n}}\)，求数列\(\{b\)\({\,\!}_{n}\)\(\}\)的通项公式．
