Question

solution pls i need fast​

Answer 1

$\color {red}\huge\bold\star\underline\mathcal{Question:-}$

$( \frac{ {x}^{a} }{ {x}^{b}})^{ \frac{1}{ab} } \times ( \frac{ {x}^{b} }{ {x}^{c}})^{ \frac{1}{bc} } \: \times ( \frac{ {x}^{c} }{ {x}^{a}})^{ \frac{1}{ac} } = 1$

$\green{\bold{\underline{\underline{Step\:by\:step\:explanation:}}}}$

we know that ,

$( \frac{ {x}^{a} }{ {x}^{b}}) = {x}^{(a - b)}$

$({x}^{a} ) \times ( {x}^{b} ) = {x}^{(a + b)}$

${x}^{0} = 1$

using all these we get,

${x}^{ \frac{(a - b)}{ab} } \times {x}^{ \frac{(b - c)}{bc} } \times {x}^{ \frac{(c - a)}{ac} } \\ \\ \\ {x}^{( \frac{a - b}{ab} + \frac{b - c}{bc} +\frac{c - a}{ac} )} \\ \\ \\ {x}^{ \frac{c(a - b) + a(b - c) + b(c - a)}{abc} } \\ \\ \\ \\ {x}^{0} = 1$

$\large\purple{\boxed{\sf Hence\:Proved}}$