Step-by-step explanation:
In order to add, subtract, multiply or divide, the order of radicals (or Surds) must be equal.
(1) ERROR IN THE SIMPLIFICATION:
Order of radicals are not made equal
(2) CORRECT SOLUTION:
[tex] \frac{ \sqrt[7]{ {x}^{5} } }{ \sqrt[4]{ {x}^{2} } } \\ \\ = \frac{ \sqrt[7 \times 4]{ {x}^{5 + 4} } }{ \sqrt[4 \times 7]{ {x}^{2 + 7} } } \\ \\ = \frac{ \sqrt[28]{ {x}^{9} } }{ \sqrt[28]{ {x}^{9} } } \\ \\ = \sqrt[28]{ \frac{ {x}^{9} }{ {x}^{9} } } \\ \\ = \sqrt[28]{ {x}^{9 - 9} } \\ \\ = \sqrt[28]{ {x}^{0} }\\
\\ =\sqrt[28]{1}\\\\= 1[/tex]
