Asked by Sofia
A class is given this question on a test about exponents: A squirrel collects 12 nuts an hour for 12 hours on 12 days. Write an expression with and without exponents to find how many nuts the squirrel collected.
Two students provided these answers.
This table presents the data collected by students A and B on the number of nuts gathered by a squirrel over a specific period of time.
Student A Student B
12^3 12^3
12⋅3 12⋅12⋅12
36 nuts 1,728 nuts
Which student is correct? Explain what the incorrect student did incorrectly.
All Answers 1
Answered by
GPT-5 mini
AI
Student B is correct.
Work:
- Nuts per hour × hours per day × days = 12 × 12 × 12.
- That is 12^3 (by definition a^3 = a·a·a), and 12·12·12 = 1,728.
- You can also compute it stepwise: 12 nuts/hour × 12 hours = 144 nuts per day; 144 × 12 days = 1,728 nuts total.
Error in Student A:
- They evaluated 12^3 as 12·3 = 36, which is wrong. 12^3 means 12 multiplied by itself three times (12·12·12), not 12 multiplied by 3. For example, 3^4 = 3·3·3·3 = 81, not 3·4 = 12.
Work:
- Nuts per hour × hours per day × days = 12 × 12 × 12.
- That is 12^3 (by definition a^3 = a·a·a), and 12·12·12 = 1,728.
- You can also compute it stepwise: 12 nuts/hour × 12 hours = 144 nuts per day; 144 × 12 days = 1,728 nuts total.
Error in Student A:
- They evaluated 12^3 as 12·3 = 36, which is wrong. 12^3 means 12 multiplied by itself three times (12·12·12), not 12 multiplied by 3. For example, 3^4 = 3·3·3·3 = 81, not 3·4 = 12.
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