Answer with explanation:
The Given Expression is
[tex]=(x^{\frac{1}{2}}*y^\frac{1}{4}*z)^{-2}\\\\=(x^{\frac{1}{2}})^{-2}\times(y^\frac{1}{4})^{-2}\times z^{-2}\\\\=x^{\frac{-2}{2}}\times y^{\frac{-2}{4}} \times z^{-2}\\\\=x^{-1}\times y^{\frac{-1}{2}}\times z^{-2}\\\\ =\frac{ y^{\frac{-1}{2}}}{x \times z^2}[/tex]
Used following law of exponents
[tex](x^a*y^b*z^c)^m=x^{am}*y^{b m}*z^{cm}[/tex]
In option C,if we replace [tex]y^{\frac{1}{2}} {\text{by}}y^{\frac{-1}{2}}[/tex]
then Option C, will be true,otherwise none of the option is true.
