A technician at a manufacturing plant is calculating a precision variance factor using the expression $(-4\sqrt[4]{9a^3})(3\sqrt[4]{27a^2})$. Arrange the steps below in the correct order to simplify this expression to its most reduced form.

A quality control technician is calculating the structural integrity of a component using the radical expression $(-4\sqrt[4]{9a^3})(3\sqrt[4]{27a^2})$. During the simplification process, the technician multiplies the terms to arrive at the intermediate form $-12\sqrt[4]{243a^5}$. To complete the simplification, the technician must identify the largest factor of the radicand that is a perfect fourth power. Which of the following is that factor?

An industrial parts technician is verifying a material stress calculation that involves the product of two radical expressions: ${}(-4\sqrt[4]{9a^3})(3\sqrt[4]{27a^2})$. Match each component of the simplification process with its correct mathematical value.

A workshop supervisor is calculating the surface area for a custom bracket using the expression $(2\sqrt{6y^4})(12\sqrt{30y})$. When this expression is simplified to its most reduced form, $Ay^2\sqrt{5y}$, what is the numerical value of the constant coefficient $A$?

A construction estimator is simplifying the expression $(2\sqrt{6y^4})(12\sqrt{30y})$ to determine the amount of material needed for a job. True or False: According to the Product Property for Radicals, the estimator can multiply the radicands ${}6y^4$ and ${}30y$ together and place the result under a single square root sign.