Question

simplify
$( \frac{x ^{a} }{ {x}^{b} } ) ^{c} \times (\frac{ {x}^{b} }{ {x}^{c} }) ^{a} \times ( \frac{ {x}^{c} }{ {x}^{a} } ) ^{b}$
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Answer 1

$\Large\mathtt{ ( \frac{x ^{a} }{ {x}^{b} } ) ^{c} × (\frac{ {x}^{b} }{ {x}^{c} }) ^{a} × ( \frac{ {x}^{c} }{ {x}^{a} } ) ^{b} }$

$\Large\mathtt{ = (\frac{x^{ac}}{x^{bc}}) × (\frac{x^{ab}}{x^{ac}}) × (\frac{x^{bc}}{x^{ab}})}$

$\large\mathtt{ = x^{ac}×x^{-bc}×x^{ab}×x^{-ac}×x^{bc}×x^{-ab} }$

$\large\mathtt{= x^{(ac-bc+ab-ac+bc-ab)}}$

$\large\mathtt{ = x^{0}}$

$\large\mathtt{ = 1}$