Simplify :

$(x^{a + b})^{a - b} . (x^{b + c})^{b - c} . (x^{c + 1})^{c - a}$

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Solution

$(x^{a + b})^{a - b} . (x^{b + c})^{b - c} . (x^{c + 1})^{c - a} = x^{(a + b) (a - b)} . x^{(b + c) (b - c)} . x^{(c + a) (c - a)} = x^{a^{2} - b^{2}} . x^{b^{2} - c^{2}} . x^{c^{2} - a^{2}} = x^{a^{2} - b^{2} + b^{2} - c^{2} + c^{2} - a^{2}} = x^{0} = 1$

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Similar questions

\frac{x^{a + b} \cdot x^{b + c} \cdot x^{c + a}}{(x^{a} \cdot x^{b} \cdot x^{c})^{2}}

Show that :

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

(x^{a + b})^{a - b} . (x^{b + c})^{b - c} . (x^{c + a})^{c - a}

{(\frac{x^{a}}{x^{- b}})}^{a - b} . {(\frac{x^{b}}{x^{- c}})}^{b - c} . {(\frac{x^{c}}{x^{- a}})}^{c - a}

{(\frac{x^{a}}{x^{b}})}^{(a^{2} + b^{2} + a b)} \times {(\frac{x^{b}}{x^{c}})}^{(b^{2} + c^{2} + c b)} \times {(\frac{x^{c}}{x^{a}})}^{(c^{2} + a^{2} + c a)}

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