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Simplify: \frac{ {x}^(a + b) . {x}^(b + c) {x}^(c + a) }{ {x}^(a). {x}^(b) . {x}^(c) } \\

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User Nero Vanbiervliet
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1 Answer

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13 votes

Explanation:


\bf \underline{Solution-} \\

We have to simplify the given expression.


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

We know that:


\rm \longmapsto {x}^(a) * {x}^(b) = {x}^(a + b)


\rm \longmapsto \frac{ {x}^(a) }{ {x}^(b) } = {x}^(a - b)

Therefore, we get:


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


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


\rm = {x}^(2(a + b+ c) - (a + b + c))


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

User Elmar Weber
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