Question

\[ \left[ \left(\frac{x^{a(a-b)}}{x^{a(a+b)}}\right) \div \left(\frac{x^{b(b-a)}}{x^{b(b+a)}}\right) \right]^{a+b} \]

Solution

\[ = \left[ \frac{x^{a(a-b)-a(a+b)}} {x^{b(b-a)-b(b+a)}} \right]^{a+b} \] \[ = \left[ \frac{x^{-2ab}}{x^{-2ab}} \right]^{a+b} \] \[ = (1)^{a+b} \] \[ = 1 \]

Answer

\[ \boxed{1} \]

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