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Find the value of `((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))`

A

`1`

B

`4`

C

`-1`

D

`2`

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The correct Answer is:
A
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Prove that: ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

Prove that. (i) sqrt(x^(-1) y) .sqrt(y^(-1) z) . Sqrt(z^(-1) x) = 1 (ii) ((1)/(x^(a-b)))^((1)/(a-c)).((1)/(x^(b-c))).((1)/(x^(c-b)))^((1)/(c-b))= 1 (iii) (x^(a(b-c)))/(x^(b(a-c))) div ((x^(b))/(x^(a))) (iv) ((x^(a+b))^(2)(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))

For any positive real number x, find the value of ((x^(a))/(x^(b)))^(a+b)x((x^(b))/(x^(c)))^(b+c)x((x^(c))/(x^(a)))^(c+a)

Find the value of the expression ((x^(a+b))^2xx (x^(b+c))^2xx(x^(c+a))^2)/(x^a x^b x^c)^4, if x=2,a=1,b=2,c=3

Show that: (x^(a(b-c)))/(x^(b(a-c)))-:((x^(b))/(x^(a)))^(c)=1((x^(a+b))(x^(b+c))^(2)(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Show that : (x^(a(b-c)))/(x^(b(a-c)))*(x^(b))/(x^(a)))^(c)=1((x^(a+b))^(2)(x^(b+c))(x^(c+a))^(2))/((x^(a)x^(b)x^(c))^(4))=1

Simplify (x^(a+b)xx x^(b+c)xx x^(c+a))/((x^(b)xx x^(b)xx x^(c))^(2))

MTG IIT JEE FOUNDATION-NUMBER SYSTEMS-EXERCISE (Multiple choice Question(Level-1))
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  20. If x=(sqrt(3)+1)/(sqrt(3)-1)+(sqrt(3)-1)/(sqrt(3)+1)+(sqrt(3)-2)/(sqrt...

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