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((a^(x^(4)))/(a^(y^(4))))^((1)/(x^2+y^2)...

`((a^(x^(4)))/(a^(y^(4))))^((1)/(x^2+y^2))xx((a^(y^(4)))/(a^(z^(4))))^((1)/(y^2+z^2))xx((az^(4))/(a^(x^(4))))^((1)/(z^2+z^2))=`________

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`((a^(x^(4)))/(a^(y^(4))))^((1)/(x^2+y^2))xx(a^(y^(4))/(a^(z^4)))^((1)/(y^2+z^2))xx((a^(z^(1)))/(a^(x^(4))))^((1)/(z^2+x^2))`
`=(a^(x^(4)))^((1)/(x^2+y^2))xx(a^(y^(4-z^4)))^((1)/(y^2+z^2))xx(a^(z^(4-x^4)))^((1)/(z^2+x^2))`
`=a((x^2-y^2)(x^2+y^2))/(x^3+y^2)xxa((y^2-z^2)(y^2+z^2))/(y^3+z^2)xxa((z^2-x^2)(z^2+x^2))/(z^3+x^2)`
`=a^(x^2-y^2+y^2-z^2+z^2-x^2)=a^0=1`
Hence , the correct option is (a).
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