Question

3√343/1000
4√81/16
5√-1/243
2√169/121
4√1/625
3√27/125

Answer 1

$\sqrt[3]{ \frac{343}{1000} }= \sqrt[3]{ \frac{7 ^{3} }{10^{3} } } = \frac{7}{10}$

$\sqrt[4]{ \frac{81}{16} }= \sqrt[4]{ \frac{ 3^{4} }{2^{4} } } = \frac{3}{2}$

$\sqrt[5]{ \frac{1}{243} } = \sqrt[5]{ \frac{1 ^{5} }{ 3^{5} } } = \frac{1}{5}$

$\sqrt{ \frac{169}{121} }= \sqrt{ \frac{13^{2} }{11^{2} } } = \frac{13}{11}$

$\sqrt[4]{ \frac{1}{625} } = \sqrt[4]{ \frac{ 1^{4} }{ 5^{4} } } = \frac{1}{5}$

$\sqrt[3]{ \frac{27}{125} } = \sqrt[3]{ \frac{ 3^{3} }{5^{3} } } = \frac{3}{5}$

Answer 2

Veamos:
3√343/1000 = 3√343 / 3√1000= 7/104√81/16        = 4√81 / 4√16       = 3/2
5√-1/243      =  5√-1 / 5√243     = -1/3
2√169/121   = 2√169 / 2√121   = 13/11
4√1/625       = 4√1  / 4√625       = 1/5
3√27/125     = 3√27 / 3√125     =3/5

Esto, considerando que la raíz es para toda la fracción