Question

Simplify the following expression. Assume variables are positive. Express your answer using rational exponents.

Answer 1

Let's simplify the expression:

`\begin{gathered} (x^{-(1)/(2)}\cdot y^{-(2)/(3)}\cdot z^(-2))^{-(1)/(2)}=x^{(-(1)/(2))(-(1)/(2))}y^{(-(2)/(3))(-(1)/(2))}z^{(-2)(-(1)/(2))} \\ =x^{(1)/(4)}y^{(1)/(3)}z \end{gathered}`

Therefore the answer is:

`x^{(1)/(4)}y^{(1)/(3)}z`