Question

simplify ...
please answer this question
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Answer 1

$\textsf{\large{\underline{Solution}:}}$

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:

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

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

Therefore, we get:

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

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

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

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

★ Which is our required answer.

$\textsf{\large{\underline{Know More}:}}$

$\rm 1. \: \: {a}^{m} \times {a}^{n} = {a}^{m + n}$

$\rm 2. \: \: ({a}^{m})^{n} = {a}^{mn}$

$\rm 3. \: \: \dfrac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

$\rm4. \: \: {a}^{m} \times {b}^{m} = {(ab)}^{m}$

$\rm5. \: \: \bigg(\dfrac{a}{b} \bigg)^{m} = \dfrac{ {a}^{m} }{ {b}^{m} }$

$\rm6. \: \: {a}^{ - n} = \dfrac{1}{ {a}^{n} }$

$\rm7. \: \: {a}^{n} = {b}^{n} \rightarrow a = b, n \neq0$

$\rm8. \: \: {a}^{m} = {a}^{n} \rightarrow m = n, a \neq 1$

Answer 2

Answer:

x^(a+b+c)

Hope it helps you