Question

Please answer this question with correct method and explanation.​

Answer 1

$( \frac{x {}^{a} }{x {}^{ - b} }) {}^{a - b} \times ( \frac{x {}^{b} }{x {}^{ - c} }) {}^{b - c} \times ( \frac{x {}^{c} }{x { }^{ - a} } ) {}^{c - a} \\ \\ = (x {}^{a - ( - b)} ) {}^{a - b} \times (x {}^{b - ( - c)}) {}^{b - c} \times (x {}^{c - ( - a)} ) {}^{c - a} \\ \\ =( x {}^{a + b} ) {}^{a - b} \times (x {}^{b + c}) {}^{b - c} \times (x {}^{c + a}) {}^{c - a} \\ \\ = x {}^{a {}^{2} - b {}^{2} } \times x {}^{b {}^{2} - c {}^{2} } \times x {}^{c {}^{2} - a {}^{2} } \\ \\ = x {}^{a {}^{2} - b {}^{2} + b {}^{2} - c {}^{2} + c {}^{2} - a {}^{2} } \\ \\ = x {}^{0} = 1 \\ \\ the \: formulas \: which \: i \: \: used \: to \: solve \: this \: question \: are \: in \: the \: above \: pic \:$

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