Answer:
C. [tex] \huge\frac{1}{3x {y}^{2} {z}^{4}}[/tex]
Step-by-step explanation:
[tex](9 {x}^{2} {y}^{4} {z}^{8} )^{ - \frac{1}{2} } \\ \\ = ( {3}^{2} {x}^{2} {y}^{4} {z}^{8} )^{ - \frac{1}{2} } \\ \\ = \frac{1}{( {3}^{2} {x}^{2} {y}^{4} {z}^{8} )^{ \frac{1}{2} }} \\ \\ = \frac{1}{(3x {y}^{2} {z}^{4})^{2 \times \frac{1}{2} } } \\ \\ = \frac{1}{3x {y}^{2} {z}^{4}} \\ \\ \red{ \bold{ \therefore \: (9 {x}^{2} {y}^{4} {z}^{8} )^{ - \frac{1}{2} } = \frac{1}{3x {y}^{2} {z}^{4}} }}\\ [/tex]
