Question

Which expression is equivalent to (x^1/2y^1/4z)^-2?

Answer 1

C. maybe.. not so sure

Answer 2

Answer with explanation:

The Given Expression is

  $=(x^{\frac{1}{2}}*y^\frac{1}{4}*z)^{-2}\\\\=(x^{\frac{1}{2}})^{-2}\times(y^\frac{1}{4})^{-2}\times z^{-2}\\\\=x^{\frac{-2}{2}}\times y^{\frac{-2}{4}} \times z^{-2}\\\\=x^{-1}\times y^{\frac{-1}{2}}\times z^{-2}\\\\ =\frac{ y^{\frac{-1}{2}}}{x \times z^2}$

Used following law of exponents

$(x^a*y^b*z^c)^m=x^{am}*y^{b m}*z^{cm}$

In option C,if we replace $y^{\frac{1}{2}} {\text{by}}y^{\frac{-1}{2}}$

then Option C, will be true,otherwise none of the option is true.