Question: Simplify: $\left ( \dfrac{x^a}{x^{-b}}\right )^{a-b} *$$\left ( \dfrac{x^b}{x^{-c}}\right) ^{b-c} *$$\left ( \dfrac{x^c}{x^{a}} \right )^{c+a}$

Solution:
Given,

$= \left ( \dfrac{x^a}{x^{-b}}\right )^{a-b} * \left ( \dfrac{x^b}{x^{-c}}\right )^{b-c} *\left ( \dfrac{x^c}{x^{-a}} \right )^{c+a}$

$= \left (x ^{a+b} \right )^{a-b} * \left (x ^{b+c} \right )^{b-c} * \left (x ^{c-a} \right )^{c+a}$

$= x^{(a+b)(a-b)} * x^{(b+c)(b-c)} * x^{(c-a)(c+a)}$

$= x^{a²-b²} * x^{b²-c²} * x^{c²-a²}$

$= x^{a² -b²+(b²-c²) + (c²-a²)}$

$= x^{a²-b²+b²-c²+c²-a²}$

$= x^0$

$= 1$
= Answer

Related Notes and Solutions:

Here is the website link to the notes of Indices.

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