Question

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Answer 1

Answer:

Hence Proved

Step-by-step explanation:

$\left(\frac{x^a}{x^{-b}}\right)^{a-b}\left(\frac{x^b}{x^{-c}}\right)^{b-c}\left(\frac{x^c}{x^{-a}}\right)^{c-a}\\\left(x^{a+b}}\right)^{a-b}\left({x^{b+c}}\right)^{b-c}\left(x^{c+a}\right)^{c-a}\\x^{(a+b)(a-b)}x^{(b+c)(b-c)}x^{(c+a)(c-a)}\\x^{a^2-b^2}x^{b^2-c^2}x^{c^2-a^2}\\x^{a^2-b^2+b^2-c^2+c^2-a^2}\\x^{0} = 1$

Properties Used:
1) $\frac{x^p}{x^{-q}} = x^{p+q}$

2) $(x^p)^q = x^{pq}$

3)$x^a\times x^b = x^{a+b}$

I hope my answer is helpful, Thank You!

Hence Proved