જો $x \ne 0 $ તો ${\left( {{{{x^l}} \over {{x^m}}}} \right)^{({l^2} + lm + {m^2})}}$${\left( {{{{x^m}} \over {{x^n}}}} \right)^{({m^2} + nm + {n^2})}}{\left( {{{{x^n}} \over {{x^l}}}} \right)^{({n^2} + nl + {l^2})}}=$
Medium
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a
(a) \({\left( {{{{x^l}} \over {{x^m}}}} \right)^{{l^2} + lm + {m^2}}}{\left( {{{{x^m}} \over {{x^n}}}} \right)^{{m^2} + nm + {n^2}}}{\left( {{{{x^n}} \over {{x^l}}}} \right)^{{n^2} + nl + {l^2}}}\)
(a) \({\left( {{{{x^l}} \over {{x^m}}}} \right)^{{l^2} + lm + {m^2}}}{\left( {{{{x^m}} \over {{x^n}}}} \right)^{{m^2} + nm + {n^2}}}{\left( {{{{x^n}} \over {{x^l}}}} \right)^{{n^2} + nl + {l^2}}}\)
\(={({x^{l - m}})^{({l^2} + lm + {m^2})}}{({x^{m - n}})^{{m^2} + nm + {n^2}}}\)\({({x^{n - l}})^{{n^2} + nl + {l^2}}}\)
\(={x^{{l^3} - {m^3}}}.{x^{{m^3} - {n^3}}}.{x^{{n^3} - {l^3}}}\)=\({x^{{l^3} - {m^3} + {m^3} - {n^3} + {n^3} - {l^3}}} = {x^0}=1\)
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