Question

Answer it properly by writing on paper....
I will mark your answer as brainliest if you're correct......​

Answer 1

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Answer 2

We know,

$\bull \: \: \boxed{ \bf \frac{ {a}^{m} }{ {a}^{n} } = {a}^{(m - n)} }$

$\bull \: \: \boxed{ \bf {a}^{m}. {a}^{n} . {a}^{p} = {a}^{(m + n + p)} }$

Now,

$\rm { \bigg \{ \frac{ {x}^{b} }{ {x}^{c} } \bigg\}}^{\big( \frac{1}{bc} \big)} .{ \bigg \{ \frac{ {x}^{c} }{ {x}^{a} } \bigg\}}^{\big( \frac{1}{ac} \big)} .{ \bigg \{ \frac{ {x}^{a} }{ {x}^{b} } \bigg\}}^{\big( \frac{1}{ab} \big)} \\ \\ \to \tt { \{ {x}^{b - c} \}}^{( \frac{1}{bc} )}. { \{ {x}^{c - a} \}}^{( \frac{1}{ac} )}. { \{ {x}^{a - b} \}}^{( \frac{1}{ab} )} \\ \\ \tt \to { \{ x\}}^{ \big( \frac{b - c}{bc} \big)} .{ \{ x\}}^{ \big( \frac{ c - a}{ac} \big)}.{ \{ x\}}^{ \big( \frac{a - b}{ab} \big)} \\ \\ \tt \to { \big\{x \big\}}^{ \big\{ \frac{b - c}{bc} + \frac{c - a}{ac} + \frac{a - b}{bc}\big\}} \\ \\ \tt \to{(x)}^{ \big\{ \frac{a(b - c) + b(c - a) + c(a - b)}{abc} \big\} } \\ \\ \tt \to {(x)}^{ \frac{ \green{ \cancel{ab}} - \purple{\cancel{ac}} + \orange{\cancel{bc}} - \green{\cancel{ba}} + \purple{\cancel{ca}} - \orange{\cancel{cb}}}{abc} } \\ \\ \to \tt {x}^{ \big(\frac{0}{abc} \big) } \\ \\ \to \tt {x}^{(0)} \: \: = \sf \red 1$

Hence,

$\large \sf{ \bigg \{ \frac{ {x}^{b} }{ {x}^{c} } \bigg\}}^{\big( \frac{1}{bc} \big)} .{ \bigg \{ \frac{ {x}^{c} }{ {x}^{a} } \bigg\}}^{\big( \frac{1}{ac} \big)} .{ \bigg \{ \frac{ {x}^{a} }{ {x}^{b} } \bigg\}}^{\big( \frac{1}{ab} \big)} \huge= \red1$