SImplify 12^x/48^2x

$$\\\frac{12^x}{48^{2x}}\\\\ =\frac{12^x}{(12*4)^{2x}}\\\\ =\frac{12^x}{12^{2x}*4^{2x}}\\\\ =\frac{1}{12^x*4^{2x}}\\\\ =\frac{1}{3^x*4^{x}*4^{2x}}\\\\ =\frac{1}{3^x*4^{3x}}\\\\ =\frac{1}{3^x*64^x}}\\\\ =\frac{1}{192^x}}\\\\$$

Maybe I have CDD           I have probably done this the long way and there might be errors.