Mathematics

Problem

Simplify the following algebraic fraction by expressing all radicals as rational exponents. Give your answer with positive exponents only. a. (i) Write

\sqrt[3]{27m^{4}}

and

\sqrt{n}

in the numerator using rational exponents. b. (ii) Simplify the numerator

\sqrt[3]{27m^{4}} \cdot \sqrt{n}

. c. (iii) Hence simplify the entire fraction

\dfrac{\sqrt[3]{27m^{4}}\,\sqrt{n}}{3m^{1/2} n^{1/4}}.

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