Question

The reciprocal of ${\left(\frac{2}{5}\right)}^{-1}$is:

• A. $\frac{2}{5}$
• B. $\frac{5}{2}$
• C. $\frac{-5}{2}$
• D. $\frac{-2}{5}$

Answer 1

The correct option is A

$\frac{2}{5}$

Step-1: Write ${\left(\frac{2}{5}\right)}^{-1}$in fraction form

By the law of exponent, we know $a^{-n}=\frac{1}{a^n}$

So, ${\left(\frac{2}{5}\right)}^{-1}$$=\frac{5}{2}$

Step-2: Find the reciprocal of $\frac{5}{2}$

Reciprocal of $\frac{5}{2}$is $\frac{1}{{\displaystyle \frac{5}{2}}}=1\times \frac{2}{5}=\frac{2}{5}$

Hence, Option $\left(a\right)$is the correct option