Essay

Product Property and Negative Exponent Rules in Circuit Attenuation

As an assistant technician at a telecommunications firm, you are reviewing a system diagnostic manual. The manual contains the mathematical expression z4z5z^{-4} \cdot z^{-5} representing signal degradation across two cable segments, where zz is the signal factor. To explain this formula to a new trainee, you need to break down the underlying algebraic rules.

In your own response, state the two fundamental exponent properties/rules required to simplify this expression (writing down their general algebraic formulas), and explain the exact step-by-step process of how they are recalled and applied to rewrite z4z5z^{-4} \cdot z^{-5} as a simplified expression with a single positive exponent.

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Updated 2026-06-18

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