Question

$x^{a}$ × $x^{b}$ × $x^{-a}$ x $x^{-b}$

Simplify

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Answer 1

Answer:

Given,

(

x

b

x

a

)

a

2

+ab+b

2

×(

x

c

x

b

)

b

2

+bc+c

2

×(

x

a

x

c

)

c

2

+ca+a

2

=(x

a−b

)

a

2

+ab+b

2

×(x

b−c

)

b

2

+bc+c

2

×(x

c−a

)

c

2

+ca+a

2

=x

a

3

+a

2

b+ab

2

−a

2

b−ab

2

−b

3

×x

b

3

+b

2

c+bc

2

−cb

2

−bc

2

−c

3

×x

c

3

+c

2

a+ca

2

−c

2

a−ca

2

−a

3

=x

a

3

−b

3

×x

b

3

−c

3

×x

c

3

−a

3

=x

a

3

−b

3

+b

3

−c

3

+c

3

−a

3

=x

0

=1 [henceproved]

Step-by-step explanation:

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