{x^(a² +b²)/x^-ab}^(a-b) * {x^(b²+bc)/ x^-c²)^(b-c) * {x^(c²+ac/x^-a²)^c -a | Indices - Simplify | SciPiPupil

Question: Simplify: $\left (\dfrac{x^{a²+b²}}{x^{-ab}} \right)^{a-b} ×$ $\left (\dfrac{x^{b²+bc}}{x^{-c²}} \right)^{b-c} ×$$\left (\dfrac{x^{c²+ac}}{x^{-a²}} \right)^{c-a} ×$

Solution:

Given,

$= \left (\dfrac{x^{a²+b²}}{x^{-ab}} \right)^{a-b} ×\left (\dfrac{x^{b²+bc}}{x^{-c²}} \right)^{b-c} ×\left (\dfrac{x^{c²+ac}}{x^{-a²}} \right)^{c-a} ×$

$= x^{(a² +ab +b²)(a-b)} × x^{(b² +bc +c²)(b-c)} × x^{(c² +ac +a²)(c-a)}$

$= x^{a³-b³} × x^{b³-c³} × x^{c³-a³}$

$= x^{(a³-b³) +(b³-c³) + (c³-a³)}$

$= x^{a³-b³+b³-c³+c³-a³}$

$= x^0$

$= 1$

= Answer

Related Notes and Solutions:

Here is the website link to the notes of Indices.

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