Question

please solve this question.. its a humble request!!

I will mark you as brainliest if you gave the correct answer.. and yes.. i need steps.. not only answer..
pls answer step wise!!! ​

Answer 1

• Refer to the attachment!
• hope it helps :)!

Answer 2

$\underline{\bf{\underline{Answer-}}}$

$\implies\large{\bf{\big( \frac{x ^{a} }{ {x}^{b} }\big) ^ \frac{1}{ab} } \times \: \big(\frac{x ^{b}}{ {x}^{c}}\big) ^{ \frac{1}{bc} }\: \times \big(\frac{x ^{c}}{ {x}^{a}}\big) ^{ \frac{1}{ca} } = 1}$

$\underline{\bf{\underline{Solution-}}}$

$\implies\large{\sf{\big( \frac{x ^{a} }{ {x}^{b} }\big) ^ \frac{1}{ab} } \times \: \big(\frac{x ^{b}}{ {x}^{c}}\big) ^{ \frac{1}{bc} }\: \times \big(\frac{x ^{c}}{ {x}^{a}}\big) ^{ \frac{1}{ca} }}$

$\implies\large{\sf{\big( x ^{a - b} \big) ^ \frac{1}{ab} } \times \: \big( {x}^{b - c} \big) ^{ \frac{1}{bc} }\: \times \: \big( {x}^{c - a} \big) ^{ \frac{1}{ca}}}$

$\implies\large{\sf{ x ^{a - b \times \frac{1}{ab}} \times \: {x}^{b - c \times \frac{1}{bc} }\: \times \:x^{c - a \times \frac{1}{ca} }}}$

$\implies\large{\sf{ x ^{ \frac{a - b}{ab}} \times \: {x}^{ \frac{b - c }{bc} }\: \times \:x^{ \frac{c - a}{ca}}}}$

$\implies\large{\sf{ x ^{ \frac{(a - b)}{ab} +\frac{(b - c) }{bc} + \frac{(c - a)}{ca}}}}$

$\implies\large{\sf{ x ^{ \frac{1}{b}-\frac{1}{a}} \times x ^{ \frac{1}{c}-\frac{1}{b}} \times x ^{ \frac{1}{a}-\frac{1}{c}}}}$

$\implies\large{\sf{ x ^{\frac{1}{b}-\frac{1}{a}+ \frac{1}{c}-\frac{1}{b}+ \frac{1}{a}-\frac{1}{c}}}}$

$\implies\large{\sf{ x^ {0}}}$

$\implies\large{\bf{1}}$

$\underline{\bf{\underline{Identities\:Applied-}}}$

$\star\:\:\:{\boxed{\bf{\:\:\frac{x^a}{x^b}=x^{a-b}}}}$

$\star\:\:\:{\boxed{\:\:\bf{(x^a)^b=x^{ab}}}}$

$\star\:\:\:{\boxed{\:\:\bf{x^a\times x^b=x^{a+b}}}}$

$\star\:\:\:{\boxed{\:\:\bf{x^0=1}}}$