1. \( \frac{2}{3} z^{-2} \)

To manipulate the expression \( \frac{2}{3} z^{-2} \), you can rewrite it in a more manageable form by applying the rule of negative exponents. This turns \( z^{-2} \) into \( \frac{1}{z^2} \), so we get \( \frac{2}{3z^2} \). Voila! That's a much friendlier format that makes it easier to understand and use in equations. Now, to pump up your math game, remember that negative exponents indicate the reciprocal. If you ever see a negative power creeping up, just flip it! So, \( z^{-n} \) becomes \( \frac{1}{z^n} \). This concept will save you lots of headaches in algebra and calculus alike!