Question
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Answer
The simplified form of \( \left(2 \cdot 10^{2}\right)^{-1} \) is \( \frac{1}{200} \) or 0.005.
Solution
To simplify the expression \( \left(2 \cdot 10^{2}\right)^{-1} \), follow these steps:
1. **Evaluate the expression inside the parentheses:**
\[
2 \cdot 10^{2} = 2 \cdot 100 = 200
\]
2. **Apply the negative exponent:**
\[
\left(200\right)^{-1} = \frac{1}{200}
\]
So, the simplified form of \( \left(2 \cdot 10^{2}\right)^{-1} \) is:
\[
\frac{1}{200}
\]
**Decimal Representation:**
\[
\frac{1}{200} = 0.005
\]
**Final Answer:**
\[
\frac{1}{200}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
First, let's break it down! The expression \( \left(2 \cdot 10^{2}\right)^{-1} \) means we need to take the reciprocal of \( 2 \cdot 10^{2} \). So, first calculate \( 2 \cdot 10^{2} = 200 \). Taking the reciprocal gives us \( \frac{1}{200} \). If you want to express this in decimal form, it equals \( 0.005 \). Now, here's a fun twist: Did you know that scientific notation is super handy when dealing with very large or very small numbers? Instead of saying "0.005", you can express the same value as \( 5 \times 10^{-3} \). This makes it easier to communicate numerical values, especially in scientific contexts where precision is key!
