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^{(2)/(5)}\implies \sqrt[5]{x^2} \\\\\\ and\implies (4ab)^{(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}`