Prove- xa-xba-b-xb-xcb-c-xc-xac-a-1

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Simplification of an Expression

Prove- xa/xb...

Question

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

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{(\frac{x^{a}}{x^{b}})}^{a + b} \times {(\frac{x^{b}}{x^{c}})}^{b + c} \times {(\frac{x^{c}}{x^{a}})}^{c + a} =

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

(\frac{x^{a}}{x^{b}}) a + b \times (\frac{x^{b}}{x^{c}}) b + c \times (\frac{x^{c}}{x^{a}}) c + a

(\frac{x^{a}}{x^{b}})^{a + b} \times (\frac{x^{b}}{x^{c}})^{b + c} \times (\frac{x^{c}}{x^{a}})^{c + a}

{(\frac{x^{a}}{x^{b}})}^{(a + b)} \times {(\frac{x^{b}}{x^{c}})}^{(b + c)} \times {(\frac{x^{c}}{x^{a}})}^{(c + a)}

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