Multiplicative inverse of `10^(-100)` is

Options

A. `(10)^(-100)`
B. `(1)/((10)^(-100) )`
C. `(10)^(-10)`
D. `(10^(-50))^3`

Answer

To find the multiplicative inverse of \( 10^{-100} \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Multiplicative Inverse**:
The multiplicative inverse (or reciprocal) of a number \( a \) is defined as \( \frac{1}{a} \).

2. **Identify the Given Number**:
In this case, the number given is \( a = 10^{-100} \).

3. **Write the Expression for the Multiplicative Inverse**:
The multiplicative inverse of \( 10^{-100} \) can be expressed as:
\[ \text{Multiplicative Inverse} = \frac{1}{10^{-100}} \]

4. **Apply the Property of Exponents**:
We know that \( a^{-m} = \frac{1}{a^m} \). Therefore, we can rewrite \( \frac{1}{10^{-100}} \) as:
\[ \frac{1}{10^{-100}} = 10^{100} \]

5. **Conclusion**:
Thus, the multiplicative inverse of \( 10^{-100} \) is:
\[ 10^{100} \]

### Final Answer:
The multiplicative inverse of \( 10^{-100} \) is \( 10^{100} \).

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