MCQ
The reciprocal of $\Big(\frac{2}{5}\Big)^{-1}$ is
- A$\frac{2}{5}$
- ✓$\frac{5}{2}$
- C$-\frac{5}{2}$
- D$-\frac{2}{5}$
✓
Answer
Correct option: B.
$\frac{5}{2}$
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^{\text{m}}} [\because$ a is non$-$integer$]$
$\therefore$ $\Big(\frac{2}{5}\Big)^{-1}=\frac{1}{\Big(\frac{2}{5}\Big)^{1}}$
$=\frac{5}{2}$
$\therefore$ $\Big(\frac{2}{5}\Big)^{-1}=\frac{1}{\Big(\frac{2}{5}\Big)^{1}}$
$=\frac{5}{2}$
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