https://file.aiquickdraw.com/mathbot/file/1728418963477mwagfqeo.jpg

The expression in the image is:

\[
\frac{100}{(-5)^2} + 16 \cdot 2^{-3}
\]

Let’s break it down step by step:

1. **Evaluate the denominator of the fraction**:  
   \((-5)^2 = 25\)

2. **Simplify the fraction**:  
   \(\frac{100}{25} = 4\)

3. **Evaluate the exponent**:  
   \(2^{-3} = \frac{1}{2^3} = \frac{1}{8}\)

4. **Multiply the result**:  
   \(16 \cdot \frac{1}{8} = 2\)

5. **Add the two results**:  
   \(4 + 2 = 6\)

So, the value of the expression is:

\[
6
\]

Would you like more details or have any questions?

Here are five related questions to expand your understanding:

1. What happens if the exponent on 2 was positive instead of negative?
2. How does changing the base of the exponent affect the result?
3. What is the general rule for evaluating negative exponents?
4. Can you simplify the same expression using a calculator?
5. How would the result change if the base of the fraction was positive?

**Tip**: Always apply the order of operations (PEMDAS) when solving such expressions—handle exponents and multiplication before addition or subtraction!

Learn how to evaluate the expression 100 / (-5)^2 + 16 * 2^(-3) step by step. This problem involves applying exponents, simplifying fractions, and using the order of operations (PEMDAS). Suitable for students in Grades 6-8.

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