Simplify the following algebraic fraction by expressing all radicals as rational exponents

MATHEMATICS · Multi-part · CBSE · Mathematics · Number Systems · Number Systems

Problem

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

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

and

\sqrt{n}

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

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

. (iii) Hence simplify the entire fraction

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