Question

Which expression is equivalent to ^4 square root

Answer 1

$\bf \sqrt[4]{\cfrac{24x^6y}{128x^4y^5}}\implies \cfrac{\sqrt[4]{4x^6y}}{\sqrt[4]{128x^4y^5}}\quad \begin{cases} 24=2\cdot 2\cdot 2\cdot 3\\ 128=2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\\ x^6=x^{4+2}\\ \qquad x^4x^2\\ y^5=y^{4+1}\\ \qquad y^4y^1 \end{cases}$

$\bf \cfrac{\sqrt[4]{\underline{2\cdot 2\cdot 2}\cdot 3\cdot \underline{x^4} x^2\underline{y}}}{\sqrt[4]{\underline{2\cdot 2\cdot 2}\cdot 2\cdot 2\cdot 2\cdot 2\cdot \underline{x^4} y^4\underline{y^1}}} \implies \cfrac{\sqrt[4]{3x^2}}{\sqrt[4]{2^4y^4}}\implies \cfrac{\sqrt[4]{3x^2}}{2y}$