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Question : The value of $(x^{b+c})^{b–c}(x^{c+a})^{c–a}(x^{a+b})^{a–b}$, where $(x\neq 0)$ is:
Option 1: 1
Option 2: 2
Option 3: –1
Option 4: 0
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Answer (1)
Correct Answer: 1
Solution :
Given: $(x^{b+c})^{b–c}(x^{c+a})^{c–a}(x^{a+b})^{a–b}$ $(x\neq 0)$
= $(x^{(b+c)×(b–c)})(x^{(c+a)(c–a)})(x^{(a+b)×(a–b)})$
= $(x^{(b^{2}–c^{2})})(x^{(c^{2}–a^{2})})(x^{(a^{2}–b^{2})})$
= $x^{(b^{2}–c^{2}+c^{2}–a^{2}+a^{2}–b^{2})}$
= $x^{0}$
= 1
Hence, the correct answer is 1.
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