Question

$\sqrt[lm]{ \frac{ {x}^{l} }{ {x}^{m} } }. \sqrt[mn]{ \frac{ {x}^{m} }{ {x}^{n} } } . \sqrt[nl]{ \frac{ {x}^{n} }{ {x}^{l} } }$
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Answer 1

AnSwer :

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$:\implies\sf{\sqrt[lm]{\dfrac{x^l}{x^m}}.\sqrt[mn]{\dfrac{x^m}{x^n}}.\sqrt[nl]{\dfrac{x^n}{x^l}}}$

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$:\implies\sf{(x^{l-m})^{\frac{1}{lm}}.(x^{m-n})^{\frac{1}{mn}}.(x^{n-l})^{\frac{1}{nl}}}$

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$:\implies\sf{x^{\frac{l-m}{lm}}.\;x^{\frac{m-n}{mn}}.\;x^{\frac{n-l}{nl}}}$

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$:\implies\sf{x\;^{(\frac{l-m}{lm}+\frac{m-n}{mn}+\frac{n-l}{nl})}}$

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$:\implies\sf{x\;^{(\frac{ln-mn+lm-ln+mn-lm}{lmn})}}$

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$:\implies\sf{x^0}$

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$:\implies\bf{1}$⠀⠀⠀