#### Question

Show that:

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

#### Solution

`{(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

Is there an error in this question or solution?

Solution Show That: `{(X^(A-a^-1))^(1/(A-1))}^(A/(A+1))=X` Concept: Laws of Exponents for Real Numbers.