QUESTION

Find out the multiplicative inverse of ${2^{ - 4}}$ is : $A.{\text{ 2}} \\ {\text{B}}{\text{. 4}} \\ {\text{C}}{\text{. }}{{\text{2}}^4} \\ D.{\text{ - 4}} \\$

Hint – In order to solve this question, we must know the identity of the multiplicative inverse that is number b is the multiplicative inverse of the number a, if a$\times$ b = 1 .

Complete step-by-step solution -
A reciprocal is a number obtained by interchanging numerator and denominator. Multiplication inverse means the same thing as reciprocal.
The product of a number and its multiplicative inverse is 1.
By using the identity $a \times b = 1$ , we get
Let us suppose that $a = {2^{ - 4}}$ and $b = {2^4}$
$=$ ${2^{4 - 4}}$ (Bases are same powers are added)
$= {2^0}$
$= 1$ (Anything raised to power 0 is equal to 1)
Therefore, the identity is $a \times b = 1$ is satisfied.
Thus, multiplicative inverse of ${2^{ - 4}}$ is ${2^4}$
Therefore, Option C is correct

Note – In this particular question, by using the identity of multiplication inverse we will get our required answer. Another method to solve this question is by using multiplicative inverse or reciprocal of a fraction $\dfrac{a}{b}$ is$\dfrac{b}{a}$ that is $\dfrac{a}{b} \times \dfrac{b}{a} = 1$ . Thus by using this approach we can solve such types of questions.