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

Question 1

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

Need help please.

Question 2

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:

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

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

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

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

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