MCQ
The value of $\frac{\text{x}^{\text{a}(\text{c}-\text{c})}}{\text{x}^{\text{b}(\text{a}-\text{c})}}\div\Big(\frac{\text{x}^\text{b}}{\text{x}^{\text{a}}}\Big)^{\text{c}}$ is:
- A$4$
- B$3$
- C$2$
- ✓$1$
✓
Answer
Correct option: D.
$1$
$\frac{\text{x}^{\text{a}(\text{c}-\text{c})}}{\text{x}^{\text{b}(\text{a}-\text{c})}}\div\Big(\frac{\text{x}^\text{b}}{\text{x}^{\text{a}}}\Big)^{\text{c}}$
$\Rightarrow\frac{\text{x}^{\text{ab}-\text{ac}}}{\text{x}^{\text{ba}-\text{be}}}\div\Big(\frac{\text{x}^{\text{bc}}}{\text{x}^{\text{ac}}}\Big)$
$\Rightarrow\text{x}^{\text{ab}-\text{ac}-\text{ab}+\text{bc}}\div\text{x}^{\text{bc}-\text{ac}}$
$\Rightarrow\text{x}^{\text{bc}-\text{ac}}\div\text{x}^{\text{bc}-\text{ac}}$
$\Rightarrow1$
$\Rightarrow\frac{\text{x}^{\text{ab}-\text{ac}}}{\text{x}^{\text{ba}-\text{be}}}\div\Big(\frac{\text{x}^{\text{bc}}}{\text{x}^{\text{ac}}}\Big)$
$\Rightarrow\text{x}^{\text{ab}-\text{ac}-\text{ab}+\text{bc}}\div\text{x}^{\text{bc}-\text{ac}}$
$\Rightarrow\text{x}^{\text{bc}-\text{ac}}\div\text{x}^{\text{bc}-\text{ac}}$
$\Rightarrow1$
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