Mark the correct alternative in the following question:

$If a b c = 0, then \frac{{\{{(x^{a})}^{b}\}}^{c}}{{\{{(x^{b})}^{c}\}}^{a}} = (a) 3 (b) 0 (c) - 1 (d) 1$

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Solution

$\frac{{\{{(x^{a})}^{b}\}}^{c}}{{\{{(x^{b})}^{c}\}}^{a}} = \frac{{(x^{a})}^{b c}}{{(x^{b})}^{a c}} [As, {(x^{m})}^{n} = x^{m n}] = \frac{x^{a b c}}{x^{a b c}} [As, {(x^{m})}^{n} = x^{m n}] = \frac{x^{0}}{x^{0}} [As, a b c = 0] = \frac{1}{1} [As, x^{0} = 1] = 1$

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