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To order these expressions from least to greatest, let's evaluate each one individually.

### Given Expressions:
1. \( 8^{-2} \)
2. \( \frac{8^{10}}{8^8} \)
3. \( (8^{-2})^{-4} \)
4. \( (8^{-2})^4 \)

### Step-by-Step Evaluation:
1. **\( 8^{-2} \):**
   \[
   8^{-2} = \frac{1}{8^2} = \frac{1}{64} \approx 0.015625
   \]

2. **\( \frac{8^{10}}{8^8} \):**
   Using the property \( \frac{a^m}{a^n} = a^{m-n} \),
   \[
   \frac{8^{10}}{8^8} = 8^{10 - 8} = 8^2 = 64
   \]

3. **\( (8^{-2})^{-4} \):**
   Using the property \( (a^m)^n = a^{m \cdot n} \),
   \[
   (8^{-2})^{-4} = 8^{-2 \cdot (-4)} = 8^8 = 16777216
   \]

4. **\( (8^{-2})^4 \):**
   Similarly,
   \[
   (8^{-2})^4 = 8^{-2 \cdot 4} = 8^{-8} = \frac{1}{8^8} = \frac{1}{16777216} \approx 5.96 \times 10^{-8}
   \]

### Ordering from Least to Greatest:
Now that we have each expression evaluated, we can list them from least to greatest:
\[
(8^{-2})^4, \; 8^{-2}, \; \frac{8^{10}}{8^8}, \; (8^{-2})^{-4}
\]

### Final Answer:
The expressions in order from least to greatest are:
\[
(8^{-2})^4, \; 8^{-2}, \; \frac{8^{10}}{8^8}, \; (8^{-2})^{-4}
\]

Would you like further details or explanations?

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Here are 5 additional questions related to this topic:
1. How would the order change if all exponents were positive?
2. What happens to each expression if the base 8 is replaced with another number?
3. Can you generalize the process to any base \(a\) for these types of expressions?
4. What are the properties of exponents used to simplify these expressions?
5. How would you express \( (8^{-2})^{-4} \) as a positive power?

**Tip:** When comparing exponential expressions, simplify each term using exponent rules to make ordering easier.

Put the expressions in order from least to greatest: 8^(-2), 8^(10)/8^8, (8^(-2))^(-4), (8^(-2))^4.

Learn how to order exponential expressions like 8^(-2), 8^(10)/8^8, (8^(-2))^(-4), and (8^(-2))^4 from least to greatest using exponent properties. This problem involves key concepts such as simplifying exponents and applying rules of exponents, suitable for students in Grades 8-10.

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