Calculate: ((16)/(x^8y))^{-(1)/(2)}

Expression: ${\left( \frac{ 16 }{ {x}^{8}y } \right)}^{-\frac{ 1 }{ 2 }}$

Express with a positive exponent using ${\left( \frac{ a }{ b } \right)}^{-n}={\left( \frac{ b }{ a } \right)}^{n}$

${\left( \frac{ {x}^{8}y }{ 16 } \right)}^{\frac{ 1 }{ 2 }}$

Use ${a}^{\frac{ m }{ n }}=\sqrt[n]{{a}^{m}}$ to transform the expression

$\sqrt{ \frac{ {x}^{8}y }{ 16 } }$

To take a root of a fraction, take the root of the numerator and denominator separately

$\frac{ \sqrt{ {x}^{8}y } }{ 4 }$

Simplify the radical expression

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