[tex]I.\\a=\dfrac{(bc^3)^2}{14}\ \ \ \ |multiply\ both\ sides\ by\ 14\\\\14a=(bc^3)^2\\\\14a=b^2c^{3\cdot2}\\\\14a=b^2c^6-\fbox{:)}\\\\II.\\14a=(bc^4)^2\\\\14a=b^2c^{4\cdot2}\\\\14a=b^2c^8-\fbox{:(}\\\\III.\\ab^{-2}=\dfrac{c^6}{14}\ \ \ \ |multiply\ both\ sides\ by\ 14\\\\14ab^{-2}=c^6\ \ \ \ |multiply\ both\ sides\ by\ b^2\\\\14ab^{-2+2}=b^2c^6\\\\14a=b^2c^6-\fbox{:)}\\\\Answer:\boxed{(E)\ I\ and\ III\ only}[/tex]
