[tex]\dfrac{\left(8x\cdot 4^{3}\right)^2}{16^3}=64\\ \\ \Leftrightarrow\,\dfrac{8^2x^2\cdot (4^{3})^2}{16^3}=64 \\ \\ \Leftrightarrow\,\dfrac{64x^2\cdot 4^{6}}{(4^2)^3}=64\\ \\ \Leftrightarrow\, \dfrac{64x^2\cdot 4^{6}}{4^6}=64\\ \\ \Leftrightarrow\,64x^2 = 64\\ \\ \Leftrightarrow\,x^2 = 1\\ \\ \Leftrightarrow\, x = \pm 1\\ \\ \Rightarrow\,\boxed{x\in \{-1,\, 1\}}[/tex]
