Question

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

Need help please.​

Answer 1

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)`