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2 years ago

%20%7Bx%7D%5E%7Bc%20%2B%20a%7D%20%7D%7B%20%7Bx%7D%5E%7Ba%7D.%20%7Bx%7D%5E%7Bb%7D%20%20.%20%7Bx%7D%5E%7Bc%7D%20%7D%20%20%5C%5C%20" id="TexFormula1" title="Simplify: \frac{ {x}^{a + b} . {x}^{b + c} {x}^{c + a} }{ {x}^{a}. {x}^{b} . {x}^{c} } \\ " alt="Simplify: \frac{ {x}^{a + b} . {x}^{b + c} {x}^{c + a} }{ {x}^{a}. {x}^{b} . {x}^{c} } \\ " align="absmiddle" class="latex-formula">
Need help please.

Mathematics

1 answer:

kozerog [31]2 years ago

7 0

Step-by-step explanation:

$\bf \underline{Solution-} \\$

We have to simplify the given expression.

$\rm = \dfrac{ {x}^{a + b} \cdot {x}^{b + c} \cdot {x}^{c + a} }{ {x}^{a} \cdot {x}^{b} \cdot {x}^{c} }$

We know that:

$\rm \longmapsto {x}^{a} \times {x}^{b} = {x}^{a + b}$

$\rm \longmapsto \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b}$

Therefore, we get:

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

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

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

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

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