remember:
[tex]\sqrt{x}=x^\frac{1}{2}[/tex]
[tex]\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}[/tex] [tex]\sqrt{ab}=(\sqrt{a})(\sqrt{b})[/tex] [tex](a^b)^c=a^{bc}[/tex] [tex]\frac{x^m}{x^n}=x^{m-n}[/tex] [tex]x^{-m}=\frac{1}{x^m}[/tex](ab)/(cd)=(a/c)(b/d)
also remember PEMDAS
so
[tex]\sqrt{\frac{72x^{16}}{50x^{36}}}[/tex]
simplify inside sqrt first
[tex]\frac{72x^{16}}{50x^{26}}=[/tex] [tex](\frac{72}{50})(\frac{x^{16}}{x^{36}}=[/tex] [tex](\frac{36}{25})(x^{16-36})=[/tex]
[tex](\frac{36}{25})(x^{-20})=[/tex]
now [tex]\sqrt{(\frac{36}{25})(x^{-20})}=[/tex] [tex](\sqrt{\frac{36}{25}})(\sqrt{x^{-20}}=[/tex] [tex](\frac{\sqrt{36}}{\sqrt{25}})((x^{-20})^\frac{1}{2})=[/tex] [tex](\frac{6}{5})(x^{-10})=[/tex] [tex](\frac{6}{5})(\frac{1}{x^{10}})=[/tex] [tex]\frac{6}{5x^{10}}[/tex] answer is first option
