Question

simplify the above question.
coz I am stuck in homework... ​

Answer 1

Explanation:

$Given, \\ L.H.S = ( \frac{x {}^{a {}^{2} } }{x {}^{ b {}^{2} } } ) {}^{ \frac{1}{a + b} } \times ( \frac{x {}^{b {}^{2} } }{x {}^{c {}^{2} } } ) {}^{ \frac{1}{b + c} } ( \frac{x {}^{c {}^{2} } }{x {}^{a {}^{2} } } ) {}^{ \frac{1}{c + a} } \\ = (x {}^{a {}^{2} - b {}^{2} } ) {}^{ \frac{1}{a + b} } \times (x {}^{b {}^{2} - c {}^{2} } ) {}^{ \frac{1}{b + c} } \times (x {}^{c {}^{2} - a {}^{2} } ) {}^{ \frac{1}{c + a} } ...( \frac{a {}^{m} }{a {}^{n} } = a {}^{m - n} ) \\ by \: using \: identity \: a {}^{2} - b {}^{2} = (a + b)(a - b) \\ (x {}^{(a + b)(a - b)} ) {}^{ \frac{1}{a + b} } \times (x {}^{(b + c)(b - c)} ) {}^{ \frac{1}{b + c} } \times (x {}^{(c + a)(c - a)} {}^{ \frac{1}{c + a} } \\ = x {}^{(a - b)} \times x {}^{(b - c)} \times x {}^{(c - a)} \\ = x {}^{(a - b) + (b - c) + (c - a)}...(a {}^{m} \times a {}^{n} = a {}^{m + n} ) \\ = x {}^{a - b + b - c + c - a} \\ = x {}^{0} \\ = 1 \\ = R.H.S.$

Hope this will help you!!