In a technical training session, you are tasked with verifying a mathematical shortcut for a calculation engine. To show why rac{1}{a^{-n}} is equivalent to $a^n$, you must arrange the following derivation steps in the correct logical order.

In a software configuration file, a system administrator needs to simplify a scaling factor represented by the expression $\frac{1}{s^{-n}}$ to ensure it is processed correctly by a legacy calculation module. According to the Property of Negative Exponents, which of the following is the correct simplified form of this expression?

A technical documentation specialist is reviewing a reference manual for algebraic properties. True or False: To derive the Property of Negative Exponents, $\frac{1}{a^{-n}} = a^n$, the specialist identifies that the first step is to substitute the denominator $a^{-n}$ with its equivalent form $\frac{1}{a^n}$ to create a complex fraction.

A software quality assurance analyst is verifying the mathematical logic for a new calculation engine. To validate the proof showing that $\frac{1}{a^{-n}} = a^n$, match each algebraic expression to its specific role in the derivation process.

A data analyst is updating the mathematical logic documentation for a legacy calculation engine. The guide details how to simplify the scaling factor $\frac{1}{a^{-n}}$. According to the established derivation steps, the expression is first rewritten as the complex fraction $\frac{1}{\frac{1}{a^n}}$. To resolve this complex fraction, the main division operation must be rewritten as ____ by the reciprocal of the denominator.