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Show That: `{(X^(A-a^-1))^(1/(A-1))}^(A/(A+1))=X` - Mathematics

Show that:

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

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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

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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 2 Exponents of Real Numbers
Exercise 2.2 | Q 4.6 | Page 25
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