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Value of \( \Large \left(X^{b-c}\right)^{b+c},\ \left(X^{c-a}\right)^{c+a},\ \left(X^{a-b}\right)^{a+b} \) is
A) 0
B) X
C) 1
D) X+1
Correct answer:
C) 1
Description for Correct answer:
\( \Large \left(X^{b-c}\right)^{b+c}. \left(X^{c-a}\right)^{c+a}. \left(X^{a-b}\right)^{a+b} \)
= \( \Large \left(X\right)^{ \left(b-c\right) \left(b+c\right)}. \left(X\right)^{ \left(c-a\right) \left(c+a\right) }. \left(X\right)^{ \left(a-b\right) \left(a+b\right) } \)
\( \Large X^{b^{2}-c^{2}}.X^{c^{2}-a^{2}}.X^{a^{2}-b^{2}} \)
= \( \Large X^{b^{2}-c^{2}+c^{2}-a^{2}+a^{2}-b^{2}} \)
=\( \Large X^{0} = 1 \)
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