Question

Prove the following:

`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1

Answer 1

L.H.S.

= `sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)`

= `sqrt(y/x) · sqrt(z/y) · sqrt(x/z)`    .....(Using (a^m)ⁿ = a^mn)

= `sqrt((y/x)(z/y)(x/z))`

= `sqrt(x^(1-1) · y^(1-1) · z^(1-1))`
= `sqrt(x^° · y^° · z^°)`
= `sqrt(1·1·1)`
= 1              ......(Using a° = 1)
= R.H.S.
Hence proved.