Question

Currently requiring a little help on this, would not mind any answer <3

Answer 1

$\bf \sqrt{\cfrac{50x^6y^3}{9x^8}}=\cfrac{5y^c\sqrt{2y}}{dx}\\\\ -------------------------------\\\\ \sqrt{\cfrac{50x^6y^3}{9x^8}}~~ \begin{cases} 50=2\cdot 25\\ \qquad 2\cdot 5^2\\ x^6=x^{3\cdot 2}\\ \qquad (x^3)^2\\ y^3=y^{2+1}\\ \qquad y^2\cdot y\\ 9=3^2\\ x^8=x^{4\cdot 2}\\ \qquad (x^4)^2 \end{cases}\implies \cfrac{\sqrt{50x^6y^3}}{\sqrt{9x^8}}\implies \cfrac{\sqrt{2\cdot 5^2(x^3)^2\cdot y^2\cdot y}}{\sqrt{3^2(x^4)^2}}$

$\bf \cfrac{5x^3y\sqrt{2y}}{3x^4}\implies \cfrac{5y\sqrt{2y}}{3x^4x^{-3}}\implies \cfrac{5y\sqrt{2y}}{3x^{4-3}}\implies \cfrac{5y^{\stackrel{\downarrow }{1}}\sqrt{2y}}{\stackrel{\downarrow }{3} x}$