Math Problem Statement
Solution
To order these expressions from least to greatest, let's evaluate each one individually.
Given Expressions:
Step-by-Step Evaluation:
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:
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: Using the property ,
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: Using the property ,
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: Similarly,
Ordering from Least to Greatest:
Now that we have each expression evaluated, we can list them from least to greatest:
Final Answer:
The expressions in order from least to greatest are:
Would you like further details or explanations?
Here are 5 additional questions related to this topic:
- How would the order change if all exponents were positive?
- What happens to each expression if the base 8 is replaced with another number?
- Can you generalize the process to any base for these types of expressions?
- What are the properties of exponents used to simplify these expressions?
- How would you express as a positive power?
Tip: When comparing exponential expressions, simplify each term using exponent rules to make ordering easier.
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Math Problem Analysis
Mathematical Concepts
Exponents
Exponent Rules
Order of Operations
Formulas
a^m / a^n = a^(m-n)
(a^m)^n = a^(m * n)
a^(-m) = 1 / a^m
Theorems
Exponent Properties
Suitable Grade Level
Grade 8-10
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