Simplify the expression. (x^3cdot z^-(1)/(2))^(3)/(5) Write your answer without using negative exponents. Assume that all variables are positive real numbers.

To simplify the expression \((x^{3} \cdot z^{-\frac{1}{2}})^{\frac{3}{5}}\), we will follow these steps:1. Apply the power of a product rule: \((ab)^m = a^m \cdot b^m\).2. Apply the power of a power rule: \((a^m)^n = a^{mn}\).Let's start with the given expression: First, apply the power of a product rule: Next, apply the power of a power rule to each term: Simplify the exponents: Since we need to write the answer without using negative exponents, we can rewrite as : Combine the terms into a single fraction: Thus, the simplified expression is: