Question

How to simplify this

`- 3(567)^(1 / 4)`

Answer 1

`\bf a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------\\\\ -3(567)^(1/ 4)\implies -3(567)^{(1)/(4)}\implies -3(\sqrt[4]{567^1})\implies -3(\sqrt[4]{567}) \\\\\\ \begin{cases} 567=3\cdot 3\cdot 3\cdot 3\cdot 7\\ \qquad 3^4\cdot 7 \end{cases}\implies -3(\sqrt[4]{3^4\cdot 7})\implies -3(3\sqrt[4]{7})\implies -9\sqrt[4]{7}`