An industrial design assistant is updating a technical manual for a water treatment facility. To ensure the formulas are compatible with simulation software that only accepts exponential notation, they must convert several radical expressions. Match each radical expression with its equivalent rational exponent form.

An inventory analyst at a logistics company is entering an efficiency formula into a database system that only recognizes rational exponents, not radical symbols. The formula includes the term ${}5\sqrt[3]{2p}$, where $p$ represents the number of processed packages. Based on the rules for converting radicals, how must the analyst correctly write this term using a rational exponent?

A wastewater treatment technician is digitizing a maintenance manual that contains the expression $\sqrt{10m}$, where $m$ represents the meter reading of a chemical feed. To enter this into the plant's new monitoring software, the technician converts it to the rational exponent form ${}10m^{\frac{1}{2}}$. This conversion is correct.

Legacy Formula Migration

A technical documentation specialist is preparing a manual for a scientific calculator. Arrange the following steps in the correct order to convert the radical expression $3\sqrt[4]{6y}$ into its equivalent rational exponent form.

A manufacturing technician is entering a calibration formula into a new software system that requires rational exponents. The original formula includes the radical expression $\sqrt{10m}$. To ensure the software calculates the value correctly, the technician must remember that the implied index is 2, and because the radicand ${}10m$ is a product of a number and a variable, it must be enclosed in ________ so that the entire expression is treated as the base.