Simplify the expression. Write the answer with positive exponents only. Assume the variable represents a nonzero real number. \[ (2 z)^{-3}= \]

To simplify the expression \((2z)^{-3}\), we first need to apply the negative exponent rule, which tells us that \(a^{-n} = \frac{1}{a^n}\). Therefore, we rewrite the expression as \(\frac{1}{(2z)^3}\). Now, we can expand \((2z)^3\) to get \(2^3 \cdot z^3\), which equals \(8z^3\). Thus, the simplified expression becomes \(\frac{1}{8z^3}\). To keep it tidy and with positive exponents only, the final result is: \[ \frac{1}{8z^3} \]