Question

Show that:

`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`

Answer 1

`{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))=x`

LHS = `{(x^(a-a^-1))^(1/(a-1))}^(a/(a+1))`

`={(x^(a-1/a))^(1/(a-1)xxa/(a+1))}`

`={x^((a^2-1)/a)}^(a/(a^2-1))`

`=x^((a^2-1)/axxa/(a^2-1))`

`=x^1`

`= x`

= RHS