Question

the value is equal to

Answer 1

c is the correct option

Answer 2

Concept:

This question requires the multiplication of exponents and some basic multiplication and division.

Given:

The following equation is given

${( \frac{x^{b} }{x^{c} })}^{\frac{1}{bc}} .{( \frac{x^{c} }{x^{a} })}^{\frac{1}{ca}}. {( \frac{x^{a} }{x^{b} })}^{\frac{1}{ab}}$

To find:

The value of ${( \frac{x^{b} }{x^{c} })}^{\frac{1}{bc}} .{( \frac{x^{c} }{x^{a} })}^{\frac{1}{ca}}. {( \frac{x^{a} }{x^{b} })}^{\frac{1}{ab}}$

Solution:

It is given that

${( \frac{x^{b} }{x^{c} })}^{\frac{1}{bc}} .{( \frac{x^{c} }{x^{a} })}^{\frac{1}{ca}}. {( \frac{x^{a} }{x^{b} })}^{\frac{1}{ab}}$

Let's simplify the given equation

$(\frac{x^{\frac{b}{bc} } }{x^{\frac{c}{bc} }}).(\frac{x^{\frac{c}{ca} } }{x^{\frac{a}{ca} }}).(\frac{x^{\frac{a}{ab} } }{x^{\frac{b}{ab} }})$

⇒$(\frac{x^{\frac{1}{c} } }{x^{\frac{1}{b} }}).(\frac{x^{\frac{1}{a} } }{x^{\frac{1}{c} }}).(\frac{x^{\frac{1}{b} } }{x^{\frac{1}{a} }})$

On simplification we get,

⇒1

Therefore the correct option is (C)