Question

[tex](x^{\frac{1}{a-b}} )^{\frac{1}{a-c}} (x^{\frac{1}{b-c}} )^{\frac{1}{b-a}}(x^{\frac{1}{c-a}} )^{\frac{1}{c-b}}=1}
[/tex]

Answer 1

♧♧HERE IS YOUR ANSWER♧♧

$(x^{\frac{1}{a-b}} )^{\frac{1}{a-c}} (x^{\frac{1}{b-c}} )^{\frac{1}{b-a}}(x^{\frac{1}{c-a}} )^{\frac{1}{c-b}} \\ \\ = {x}^{ \frac{1}{(a - b)(a - c)} } \times {x}^{ \frac{1}{(b - c)(b - a)} } \times {x}^{ \frac{1}{(c - a)(c - b)} } \\ \\ = {x}^{ \frac{1}{ - (a - b)(c - a)} } \times {x}^{ \frac{1}{ - (b - c)(a - b)} } \times {x}^{ \frac{1}{ - (c - a)(b - c)} } \\ \\ = {x}^{ \frac{ - 1}{(a - b)(c - a)} + \frac{ - 1}{(b - c)(a - b)} + \frac{ - 1}{(c - a)(b - c)} } \\ \\ = { x}^{ \frac{ - (b - c) - (c - a) - (a - b)}{(a - b)(b - c)(c - a)} } \\ \\ = {x}^{ \frac{ - b + c - c + a - a + b}{(a - b)(b - c)(c - a)} } \\ \\ = {x}^{ \frac{0}{(a - b)(b - c)(c - a)} } \\ \\ = {x}^{0} \\ \\ = 1$

(Proved)

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