Question

Convert the rational expression to a radical...don't mind the answers I put I just need someone to show me how they do it step by step

Answer 1

$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -----------------------------\\\\ thus\implies x^{\frac{2}{5}}\implies \sqrt[5]{x^2} \\\\\\ and\implies (4ab)^{\frac{3}{5}}\implies \sqrt[5]{(4ab)^3}\implies \sqrt[5]{4^3a^3b^3} \\\\ -----------------------------\\\\ now\\\\ 4\to 2^2\qquad and\qquad 4^3\to (2^2)^3\to 2^{2\cdot 3}\to 2^6\to 2^{5+1}\to 2^52^1\\\\ -----------------------------$

$\bf \sqrt[5]{4^3a^3b^3}\implies \sqrt[5]{2^52^1a^3b^3}\implies 2\sqrt[5]{2a^3b^3}$