Prove that : (i) (xaxb)1ab(xbxc)1bc(xcxa)1ca=1(ii) 11+xa−b+11+xb−a

1.	Prove that : (i) (xaxb)1ab(xbxc)1bc(xcxa)1ca=1(ii) 11+xa−b+11+xb−a=1
Answer» Prove that : $(i) {(\frac{x^{a}}{x^{b}})}^{\frac{1}{a b}} {(\frac{x^{b}}{x^{c}})}^{\frac{1}{b c}} {(\frac{x^{c}}{x^{a}})}^{\frac{1}{c a}} = 1 (i i) \frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

Prove that : (i) (xaxb)1ab(xbxc)1bc(xcxa)1ca=1(ii) 11+xa−b+11+xb−a=1

Answer»

Prove that :

$(i) {(\frac{x^{a}}{x^{b}})}^{\frac{1}{a b}} {(\frac{x^{b}}{x^{c}})}^{\frac{1}{b c}} {(\frac{x^{c}}{x^{a}})}^{\frac{1}{c a}} = 1 (i i) \frac{1}{1 + x^{a - b}} + \frac{1}{1 + x^{b - a}} = 1$

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Prove that : (i) (xaxb)1ab(xbxc)1bc(xcxa)1ca=1(ii) 11+xa−b+11+xb−a=1

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