MCQ
For non-zero numbers a and b, $\big(\frac{\text{a}}{\text{b}}\big)^{\text{m}}\div\big(\frac{\text{a}}{\text{b}}\big)^{\text{n}}$ where $m > n$, is equal to:
  • A
    $\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{mn}}$
  • B
    $\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{m+n}}$
  • $\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{m-n}}$
  • D
    $\bigg(\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{m}}\bigg)^{\text{n}}$

Answer

Correct option: C.
$\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{m-n}}$

We know that,
$\text{a}^{\text{m}}+\text{a}^{\text{n}}=\text{a}^{\text{m-n}}(\text{m}>\text{n})$
So, $\Big(\frac{\text{a}}{\text{b}}\Big)+\Big(\frac{\text{a}}{\text{b}}\Big)^{\text{n}}=\Big(\frac{\text{a}{}}{\text{b}}\Big)^{\text{m-n}}$

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