Question

please answer me fast ​

Answer 1

$\hline \begin{array}{ ||c||} \underline{\underline{\footnotesize \tt{Used \: law \: Exponent}}}\\ \footnotesize \tt{{a}^{m} \times {a}^{n} = {a}^{m + n} } \\ \footnotesize \tt{ {a}^{m} \div {a}^{n} = {a}^{m - n} }\\ \underline{\underline{\footnotesize \tt{{a}^{0} = 1}}}\end{array}$

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$\dashrightarrow\sf{Solution:-}$

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$\dashrightarrow\tt{( \frac{ {x}^{a} }{ {x}^{b} } )^{a + b} \times( \frac{ {x}^{b} }{{x}^{c} } )^{b + c} \times( \frac{ {x}^{c} }{ {x}^{a} })^{c + a} }$

$\dashrightarrow \footnotesize \tt{ ({x}^{a - b}) ^{a + b} \times ({x}^{b - c}) ^{b + c} \times( {x}^{c - a} )^{c + a} }$

$\dashrightarrow\footnotesize \tt{{x}^{(a - b)(a + b)} \times{x}^{(b - c)(b + c)} \times {x}^{(c - a)(c + a)} }$

$\dashrightarrow \footnotesize \tt{{x}^{a(a + b) - b(a + b)} \times{x}^{b (b + c) - c(b + c)} \times {x}^{c (c + a) - a(c + a)} }$

$\dashrightarrow \footnotesize \tt{{x}^{ {a}^{2} + ab -ab - {b}^{2} } \times{x}^{ {b}^{2} + bc - bc - {c}^{2} } \times {x}^{ { c}^{2} + ac - ac - {a}^{2} } }$

$\dashrightarrow\footnotesize \tt{{x}^{ {a}^{2} + \cancel{ab} \cancel{-ab} - {b}^{2} } \times{x}^{ {b}^{2} + \cancel{bc} \cancel{ - bc } - {c}^{2} } \times {x}^{ { c}^{2} + \cancel {ac } \cancel{- ac } - {a}^{2} } }$

$\dashrightarrow\footnotesize \tt{{x}^{ {a}^{2} - {b}^{2} } \times{x}^{ {b}^{2} - {c}^{2} } \times {x}^{ { c}^{2} - {a}^{2} } }$

$\dashrightarrow \footnotesize \tt{{x}^{ {a}^{2} - {b}^{2} + {b}^{2} - {c}^{2} + { c}^{2} - {a}^{2} } }$

$\dashrightarrow \footnotesize \tt{{x}^{ \cancel {a}^{2} - \cancel {b}^{2} + \cancel {b}^{2} - \cancel{c}^{2} + \cancel { c}^{2} - \cancel {a}^{2} } }$

$\dashrightarrow \footnotesize \tt{x}^{ 0 }$

$\boxed{ \underline{\underline{ \dashrightarrow\footnotesize \tt{1 }}}}$

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