Absolute difference of small powers: What is the absolute difference between 2^3 and 3^2?

Introduction / Context:
The original phrasing “difference between” can be ambiguous in sign. By the Recovery-First Policy, we interpret it as absolute difference because MCQ options list positive numbers. We compare 2^3 and 3^2, two familiar small powers.

Given Data / Assumptions:

• 2^3 = 8
• 3^2 = 9
• Report absolute difference |8 − 9|.

Concept / Approach:
Compute both powers exactly and subtract. Taking the absolute value avoids sign confusion and matches the positive options provided.

Step-by-Step Solution:
2^3 = 83^2 = 9Absolute difference = |8 − 9| = 1

Verification / Alternative check:
Reverse order: |9 − 8| = 1 gives the same result, confirming independence from order.

Why Other Options Are Wrong:
2, 3, 5, 0 do not equal the magnitude of the difference here.

Common Pitfalls:
Reporting −1 instead of 1; in word problems “difference” often implies magnitude unless directed otherwise.

Final Answer:
1