Question

The multiplicative inverse of ${{13}^{-4}}$ is
A. $-{{13}^{4}}$
B. $-{{13}^{-4}}$
C. ${{13}^{4}}$
D. $\dfrac{1}{{{13}^{4}}}$

Answer 1

Hint: First of all we will have to know about the multiplicative inverse of any number. The multiplicative inverse of any number, let the number be $x$ , is equal to $\dfrac{1}{x}\ or\ {{x}^{-1}}$. It is also called the reciprocal of a number.

Complete step-by-step answer:
We have been asked to find the multiplicative inverse of the number ${{13}^{-4}}$.
We know that the multiplicative inverse of any number $x$ is equal to $\dfrac{1}{x}\ or\ {{x}^{-1}}$. Multiplicative inverse is also known as reciprocal of a number.
So, we can write the multiplicative inverse of the given number ${{13}^{-4}}$ as $\dfrac{1}{{{13}^{-4}}}$.
Now, we also know that we can write any number raised to a negative power, i.e. ${{x}^{-1}}$ as $\dfrac{1}{x}$. So, we can again simplify the obtained multiplicative inverse as
$\Rightarrow \dfrac{1}{{{13}^{-4}}}={{13}^{4}}$
Therefore, the correct option of the given question is option C.

Note: Remember the fact that a number is multiplied by its own multiplicative inverse the resultant value is equal to 1. Also, remember that 1 is called the multiplicative identity. Remember the property that multiplicative inverse of a unit fraction will be the values present in the denominator. We can also solve this question using another approach. We can first write the given number ${{13}^{-4}}$ as $\dfrac{1}{{{13}^{4}}}$using the fact that ${{x}^{-1}}$ can also be written as $\dfrac{1}{x}$. Then, we can apply the concept of multiplicative inverse and get the multiplicative inverse of $\dfrac{1}{{{13}^{4}}}$as ${{13}^{4}}$. So, we get the answer.