[tex]4\sqrt{32}\cdot(\frac{1}{2})^{\frac{5}{2}}\cdot(\frac{1}{64})^{-2}=\\\\=2^{2}\cdot\sqrt{16\cdot2}}\cdot2^{-\frac{5}{2}}\cdot((\frac{1}{2})^{6})^{-2}=\\\\=2^{2}\cdot4\cdot\sqrt{2}\cdot2^{-\frac{5}{2}}\cdot(2^{-6})^{-2}=\\\\=2^{2}\cdot2^{2}\cdot2^{\frac{1}{2}}\cdot2^{-\frac{5}{2}}\cdot2^{12}=\\\\=2^{2+2+\frac{1}{2}-\frac{5}{2}+12}=\\\\=2^{^{16-\frac{4}{2}}}=\\\\=2^{16-2} = 2^{14}[/tex]