Division with Mixed Index and Power of Radicand (Fraction) - Radical over Radical (Level 1)

This math topic focuses on simplifying radical expressions, specifically handling division of radicals with different indices and powers of the radicands. The expressions involve operations such as the nth root of a number raised to a power, divided by another nth root of a different number also raised to a power. The problems are designed to challenge understanding of manipulating and simplifying radical over radical expressions, converting them into simplified fractional forms. The topic is a component of a larger unit dedicated to simplifying radicals. Each question offers multiple choice answers requiring students to select the correct simplified form of the given radical expressions.

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Division with Mixed Index and Power of Radicand (Fraction) - Radical over Radical

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What does this radical expression simplify to?

272212523\frac{\sqrt[2]{27^{2} }}{\sqrt[3]{125^{2} }}

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