Question

can you solve these 2parts
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Answer 1

First of all understand that ,

$\sqrt[a]{b} = {b}^{ \frac{1}{a} } \\ \\ {c}^{a} \times {b}^{a} = {(cb)}^{a} \\ \\ { {(x}^{a} )}^{b} = {x}^{ab}$

This law of exponent shall be used to prove those identities asked by you ;

$1.\sqrt[n]{x} \sqrt[n]{y} \\ \\ = {x}^{ \frac{1}{n} } \times {y}^{ \frac{1}{n} } \\ \\ = {xy}^{ \frac{1}{n} } \\ \\ = \sqrt[n]{xy}$

$2. \sqrt[ \sqrt[n]{m} ]{x} \\ \\ = {({x}^{ \frac{1}{m} }})^{ \frac{1}{n} } \\ \\ = {x}^{ \frac{1}{mn} } \\ \\ = \sqrt[mn]{x} \\ \\ = {x}^{ \frac{1}{mn} } \\ \\ = {x}^{ { (\frac{1}{m}) }^{ \frac{1}{n} } } \\ \\ = \sqrt[ \sqrt[n]{m} ]{x}$