Question

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Answer 1

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:

$\frac{ \sqrt[7]{ {x}^{5} } }{ \sqrt[4]{ {x}^{2} } } \\ \\ = \frac{ \sqrt[7 \times 4]{ {x}^{5 + 4} } }{ \sqrt[4 \times 7]{ {x}^{2 + 7} } } \\ \\ = \frac{ \sqrt[28]{ {x}^{9} } }{ \sqrt[28]{ {x}^{9} } } \\ \\ = \sqrt[28]{ \frac{ {x}^{9} }{ {x}^{9} } } \\ \\ = \sqrt[28]{ {x}^{9 - 9} } \\ \\ = \sqrt[28]{ {x}^{0} }\\\\ =\sqrt[28]{1}\\\\= 1$