To solve the expression \( \frac{1}{2\pi} \times 5 \times 10^3 \times 0.01 \times 10^{-16} \), we can follow these steps:

1. Simplify the constants:
   \[
   \frac{1}{2\pi}
   \]

2. Multiply the numbers:
   \[
   5 \times 10^3 \times 0.01 \times 10^{-16}
   \]

Let's calculate this step-by-step:

1. First, handle the constants:
   \[
   \frac{1}{2\pi} \approx \frac{1}{6.2832} \approx 0.15915
   \]

2. Now multiply \( 5 \times 10^3 \times 0.01 \times 10^{-16} \):
   - \( 10^3 = 1000 \)
   - \( 0.01 = 10^{-2} \)
   - \( 5 \times 1000 = 5000 \)
   - \( 5000 \times 10^{-2} = 50 \)
   - \( 50 \times 10^{-16} = 50 \times 10^{-16} = 5 \times 10^{-15} \)

3. Multiply the results:
   \[
   0.15915 \times 5 \times 10^{-15} = 0.79575 \times 10^{-15} = 7.9575 \times 10^{-16}
   \]

So, the final result is:
\[
7.9575 \times 10^{-16}
\]

Would you like more details or have any questions about this calculation?

Here are 5 related questions you might find interesting:
1. How would the result change if the exponent \(10^3\) was different?
2. What happens if we replace \(2\pi\) with \(4\pi\) in the denominator?
3. How can we interpret the result in terms of orders of magnitude?
4. How would the calculation change if there were additional constants involved?
5. How do we handle calculations involving complex numbers instead of real numbers?

**Tip:** When dealing with very large or very small numbers, using scientific notation can simplify calculations and help avoid errors.

Explore the step-by-step solution to the expression 1/2π*5*10^3*0.01*10^-16. This problem covers key concepts in scientific notation and multiplication of constants. Suitable for high school students in Grades 9-12.

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