${\left( \frac{ 12x{y}^{2} }{ x\sqrt{ x } } \right)}^{-2}$
Cancel out the common factor $x$${\left( \frac{ 12{y}^{2} }{ \sqrt{ x } } \right)}^{-2}$
Express with a positive exponent using ${\left( \frac{ a }{ b } \right)}^{-n}={\left( \frac{ b }{ a } \right)}^{n}$${\left( \frac{ \sqrt{ x } }{ 12{y}^{2} } \right)}^{2}$
To raise a fraction to a power, raise the numerator and denominator to that power$\frac{ x }{ 144{y}^{4} }$