Evaluate: ((12xy^2)/(sqrt(x^3)))^{-2}

Expression: ${\left( \frac{ 12x{y}^{2} }{ \sqrt{ {x}^{3} } } \right)}^{-2}$

Simplify the radical expression

${\left( \frac{ 12x{y}^{2} }{ x\sqrt{ x } } \right)}^{-2}$

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

$\frac{ x }{ 144{y}^{4} }$