A technician is calculating the total inventory for two different product categories. Category A quantities are ${}5\sqrt[3]{y}$ and ${}4\sqrt[3]{y}$. Category B quantities are ${}7\sqrt[4]{x}$ and ${}2\sqrt[4]{y}$. Based on the rules for 'like radicals,' which statement correctly identifies which category can be simplified and what the resulting total is?

A warehouse manager is evaluating storage requirements for two sets of materials based on their volume formulas. Match each volume expression with the correct description of its simplification based on the rules for 'like radicals.'

A quality assurance analyst is reviewing a technical formula that includes the expression ${}7\sqrt[4]{x} - 2\sqrt[4]{y}$. The analyst correctly concludes that the expression cannot be simplified because, while the terms have the same index, they do not have the same ____.

A logistics coordinator is reviewing a formula for material volume that contains the expression ${}7\sqrt[4]{x} - 2\sqrt[4]{y}$. True or False: These two terms are considered 'like radicals' because they share the same radical index of 4.

A quality control technician is verifying a formula in a technical manual that includes the expression ${}5\sqrt[3]{y} + 4\sqrt[3]{y}$. Arrange the steps in the correct order to determine if these are 'like radicals' and simplify the expression correctly.