In your role as a technical documentation editor for a tool manufacturing company, you are updating the machinery manual to ensure all formulas are compatible with new digital formatting standards. Match each radical expression with its equivalent rational exponent form.

As a process engineer at a manufacturing plant, you are migrating formulas from a legacy paper system to a new digital dashboard. The dashboard does not support radical symbols and requires all expressions to be written using rational exponents. How should the formula ${}8\sqrt[3]{2a}$ be entered into the system?

A logistics coordinator at a shipping facility is updating a storage capacity formula in a database that only accepts rational exponents. To correctly convert the radical expression ${}8\sqrt[3]{2a}$ for the system, the coordinator should enter it as ${}8(2a)^{\frac{1}{3}}$.

Updating Legacy Maintenance Formulas

As an inventory specialist at a manufacturing plant, you are migrating old storage capacity formulas into a new software system. The software requires all radical expressions to be written using rational exponents. When converting the formula $\sqrt[7]{3k}$ into this new format, the entire term ${}3k$ becomes the base and must be raised to the power of ____.