Question

Write the value of . . . . Answer photo me dena

Answer 1

answer for the given problem is given

Answer 2

Question:-

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

Solution:-

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

use this exponential law

$\rm \frac{x {}^{m} }{x {}^{n} } = x {}^{m - n}$

$\rm(x {}^{m} ) {}^{n} = x {}^{m \times n}$

$\rm \: x {}^{m} \times x {}^{n} = {x}^{m + n}$

$\rm \: {x}^{0} = 1$

We get

$\rm \: ( {x}^{a - b} ) {}^{a + b} \times ( {x}^{b - c} ) {}^{b + c} \times ( {x}^{c - a} ) {}^{c + a}$

$\rm \: ( {x})^{(a - b)} {}^{(a + b)} \times ( {x})^{(b - c)} {}^{(b + c)} \times ( {x})^{(c - a)} {}^{(c + a)}$

$\rm \: ( {x})^{(a ^{2} - b ^{2} )} \times ( {x})^{(b ^{2} - c ^{2} )} \times ( {x})^{(c ^{2} - a ^{2} )}$

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

$\rm \: ( {x})^{ \not \: a ^{2} - \not b ^{2} } \ ^{ + \: \not b ^{2} - \not c ^{2} } \ ^{+ \not c ^{2} - \not a ^{2} }$

$\rm \: {x}^{0} = 1$