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((a^x)/(a^y))^(z)xx((a^y)/(a^z))^(x)xx((...

`((a^x)/(a^y))^(z)xx((a^y)/(a^z))^(x)xx((a^z)/(a^x))^(y)=____(a ne 0 and a ne 1)`

A

1

B

0

C

`a^(xyz)`

D

`a^(xy+yz+zx)`

Text Solution

Verified by Experts

The correct Answer is:
A
`((a^x)/(a^y))^(z)xx((a^y)/(a^z))^(x)xx((a^z)/(a^x))^(y)`
`=(a^(x-y))^zxx(a^(y-z))^x xx(a^(z-x))^y`
`=(a^(az-yz))^zxx(a^(yz-zx))^x xx(a^(2y-xy))`
`=a^(xz-yz+yx-zx+zy-xy)=a^0=1`
Hence the correct option is (c).
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