Question

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

A. x^1/2/yz^2

B. x^1/2/yz^2

C. y^1/2/xz^2

D. xz^2/y^1/2

Answer 1

C. maybe.. not so sure

Answer 2

Answer with explanation:

The Given Expression is

`=(x^{(1)/(2)}*y^(1)/(4)*z)^(-2)\\\\=(x^{(1)/(2)})^(-2)*(y^(1)/(4))^(-2)* z^(-2)\\\\=x^{(-2)/(2)}* y^{(-2)/(4)} * z^(-2)\\\\=x^(-1)* y^{(-1)/(2)}* z^(-2)\\\\ =\frac{ y^{(-1)/(2)}}{x * 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^{(1)/(2)} {\text{by}}y^{(-1)/(2)}`

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