For x ne 0,left( frac{x^l}{x^m} right)^{(l^2 | vedclass

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(A) Given expression: $\left( \frac{x^l}{x^m} \right)^{l^2 + lm + m^2} \left( \frac{x^m}{x^n} \right)^{m^2 + nm + n^2} \left( \frac{x^n}{x^l} \right)^

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$1$

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(A) Given expression: $\left( \frac{x^l}{x^m} \right)^{l^2 + lm + m^2} \left( \frac{x^m}{x^n} \right)^{m^2 + nm + n^2} \left( \frac{x^n}{x^l} \right)^{n^2 + nl + l^2}$ Using the law of exponents $\frac{x^a}{x^b} = x^{a-b}$,we get: $= (x^{l-m})^{(l^2 + lm + m^2)} (x^{m-n})^{(m^2 + nm + n^2)} (x^{n-l})^{(n^2 + nl + l^2)}$ Using the identity $(a-b)(a^2 + ab + b^2) = a^3 - b^3$: $= x^{l^3 - m^3} \cdot x^{m^3 - n^3} \cdot x^{n^3 - l^3}$ Using the law of exponents $x^a \cdot x^b = x^{a+b}$: $= x^{(l^3 - m^3 + m^3 - n^3 + n^3 - l^3)}$ $= x^0 = 1$

For $x \ne 0$,$\left( \frac{x^l}{x^m} \right)^{(l^2 + lm + m^2)} \left( \frac{x^m}{x^n} \right)^{(m^2 + nm + n^2)} \left( \frac{x^n}{x^l} \right)^{(n^2 + nl + l^2)} = $

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