If \[\mathbf{3600 = }{{\mathbf{2}}^{\mathbf{m}}}\,\mathbf{x }{{\mathbf{3}}^{\mathbf{n}}}\mathbf{ x}\,{{\mathbf{5}}^{\mathbf{p}}}\], then find the value of \[\frac{\mathbf{512}}{{{\mathbf{(16)}}^{\mathbf{(m+n)-p}}}}\]

• A. \[{{2}^{-7}}\]
• B. \[~{{2}^{7}}\]
• C. \[~{{2}^{8}}\]
• D. \[~{{2}^{-8}}\]
• E.  None of these