A laboratory technician uses the formula ${}3ab^2$ to determine a chemical concentration adjustment. If the concentration coefficient $a$ is $-\frac{2}{3}$ and the temperature variance $b$ is $-\frac{1}{2}$, what is the final value of the adjustment factor?

As a data technician programming a new inventory system, you need to write a script that evaluates the specific packaging metric formula ${}3ab^2$ for inputs $a = -\frac{2}{3}$ and $b = -\frac{1}{2}$. To ensure the calculation follows the correct order of operations, arrange the following steps in the exact sequence they must be performed.

A quality control technician uses the formula ${}3ab^2$ to calculate a material stress factor. For a specific test, the technician must evaluate the formula for $a = -\frac{2}{3}$ and $b = -\frac{1}{2}$. Match each operation in the evaluation process with its correct numerical value.

Industrial Efficiency Calculation

A quality control technician uses the expression ${}3ab^2$ to determine a material variance coefficient. If the primary variable $a$ is $-\frac{2}{3}$ and the secondary variable $b$ is $-\frac{1}{2}$, the technician correctly determines that the final simplified value of the coefficient is $-\frac{1}{2}$.

A catering manager at a convention center uses the contract price adjustment formula ${}3ab^2$ to determine final service fee surcharges or discounts for large banquets. In this formula, $a$ represents the seasonal hospitality demand coefficient and $b$ represents the regional culinary ingredient cost variance. During a specific off-season booking, the manager calculates that the demand coefficient $a$ is $-\frac{2}{3}$ and the ingredient variance $b$ is $-\frac{1}{2}$.

What is the final simplified price adjustment factor calculated by the manager? (Enter your answer as a simplified fraction, such as -1/2, or as a decimal, such as -0.5)