MCQ
The value of $\left(x^{a-b}\right)^{a+b} \times\left(x^{b-c}\right)^{b+c} \times\left(x^{c-a}\right)^{c+a}$ is:
- A$0$
- ✓$1$
- C$3$
- D$2$
✓
Answer
Correct option: B.
$1$
$\left(x^{a-b}\right)^{a+b} \times\left(x^{b-c}\right)^{b+c} \times\left(x^{c-a}\right)^{c+a}$
$\Rightarrow\text{x}^{\text{a}^{2}-\text{b}^2}\times\text{x}^{\text{b}^2-\text{c}^2}\times\text{x}^{\text{c}^2-\text{a}^2}$
$\Rightarrow\text{x}^{\text{a}^2-\text{b}^2+\text{b}^2-\text{c}^2+\text{c}^2-\text{a}^2}$
$\Rightarrow\text{x}^0=1$
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