Question

find the value of the given question ​

Answer 1

Answer:-

1

Step By Step Solution:-

$\sf \small \big(\frac{ {x}^{a} }{ {x}^{b} } \big)^{a + b} \times \big(\frac{ {x}^{b} }{ {x}^{c} } \big)^{b + c} \times \big(\frac{ {x}^{c} }{ {x}^{a} } \big)^{c + a}$

$\sf \small=\big( {x}^{a - b} \big)^{a + b} \times \big({x}^{b - c}\big)^{b + c} \times \big( {x}^{c - a} \big)^{c + a}$

$\sf \small = {x}^{ {a}^{2} - {b}^{2} } \times {x}^{ {b}^{2} - {c}^{2} } \times {x}^{ {c}^{2} - {a}^{2} }$

$\sf \small = {x}^{ {a}^{2} - {b}^{2} + {b}^{2} - {c}^{2} +{c}^{2} - {a}^{2}}$

$\sf \small = {x}^{0}$

$\sf \small = 1$

Hence, the required answer is 1.