Math, asked by asityadav333, 7 months ago

Answer it properly by writing on paper....
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Answered by kajalamrita09
2

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Answered by amankumaraman11
1

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

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