In a technical design workshop, you are asked to demonstrate how the scaling factor $\left(\frac{3}{4}\right)^{-2}$ is derived to be equivalent to $\left(\frac{4}{3}\right)^2$. Arrange the following steps of the derivation in the correct logical order.

In a laboratory quality control process, a researcher calculates a concentration adjustment factor of $\left(\frac{3}{4}\right)^{-2}$. Based on the step-by-step derivation of this expression using the negative exponent rule, which of the following is the final simplified equivalent?

In a logistics quality-control assessment, a coordinator uses the factor $\left(\frac{3}{4}\right)^{-2}$ to adjust shipping volume ratios. To ensure the calculation is correct, the coordinator follows a step-by-step derivation. Match each stage of the derivation with its mathematically equivalent expression.

In an environmental engineering report, a technician uses the expression $\left(\frac{3}{4}\right)^{-2}$ to represent a water filtration efficiency ratio. According to the Quotient to a Negative Exponent Property, this expression is mathematically equivalent to $\left(\frac{4}{3}\right)^2$.

A drafting technician is entering dimensional tolerance formulas into a CAD system and needs to simplify the expression $\left(\frac{3}{4}\right)^{-2}$. Based on the derivation of the quotient to a negative exponent property, the technician recalls that raising a fraction to a negative exponent gives the exact same result as raising the ________ of that fraction to the corresponding positive exponent.

Identifying the Initial Property in Scaling Calculations

Deriving Sizing Factors in Solar Array Reports