Question
Maude evaluated the expression (32)–3.
1. 32 • (−3)
2. 36
3. 729
Analyze Maude’s work. Is she correct? If not, what was her mistake?
Yes, she is correct.
No, she should have added the exponents instead of multiplying.
No, her exponent should be a negative value
No, when evaluating 36, she should have found the product of 3 and 6.
1. 32 • (−3)
2. 36
3. 729
Analyze Maude’s work. Is she correct? If not, what was her mistake?
Yes, she is correct.
No, she should have added the exponents instead of multiplying.
No, her exponent should be a negative value
No, when evaluating 36, she should have found the product of 3 and 6.
Answers
GPT-4o mini
Let's analyze the expression \((32)^{-3}\) and what Maude evaluated:
The expression \((32)^{-3}\) means \( \frac{1}{(32)^3} \).
Now let’s break down what she seems to have evaluated:
1. \(32 \cdot (-3)\) is not an appropriate interpretation of the exponent. The correct interpretation requires evaluating \(32\) raised to the power of \(-3\).
2. \(36\) seems to be a misunderstanding. If she had meant to evaluate \(32^{-3}\), that is not equal to \(36\).
3. \(729\) is \(9^3\), and is incorrect in the context of \(32^{-3}\).
Thus, looking at the options regarding her correctness:
- **No, she should have added the exponents instead of multiplying.** This is incorrect since we are working with a single base and a single exponent.
- **No, her exponent should be a negative value.** This statement is not wrong but doesn’t address her specific mistake.
- **No, when evaluating \(36\), she should have found the product of \(3\) and \(6\).** This statement is not related to the problem.
The best assessment would be **No, she should have computed \(32^{-3}\) as \(\frac{1}{(32)^3}\)**, which correctly evaluates to a different result, though not listed in the provided options. However, the closest valid critique from the answers is that she misinterpreted the meaning of the negative exponent.
So, the correct determination would be that she is not correct, as her evaluation processes do not reflect the rules for handling negative exponents.
The expression \((32)^{-3}\) means \( \frac{1}{(32)^3} \).
Now let’s break down what she seems to have evaluated:
1. \(32 \cdot (-3)\) is not an appropriate interpretation of the exponent. The correct interpretation requires evaluating \(32\) raised to the power of \(-3\).
2. \(36\) seems to be a misunderstanding. If she had meant to evaluate \(32^{-3}\), that is not equal to \(36\).
3. \(729\) is \(9^3\), and is incorrect in the context of \(32^{-3}\).
Thus, looking at the options regarding her correctness:
- **No, she should have added the exponents instead of multiplying.** This is incorrect since we are working with a single base and a single exponent.
- **No, her exponent should be a negative value.** This statement is not wrong but doesn’t address her specific mistake.
- **No, when evaluating \(36\), she should have found the product of \(3\) and \(6\).** This statement is not related to the problem.
The best assessment would be **No, she should have computed \(32^{-3}\) as \(\frac{1}{(32)^3}\)**, which correctly evaluates to a different result, though not listed in the provided options. However, the closest valid critique from the answers is that she misinterpreted the meaning of the negative exponent.
So, the correct determination would be that she is not correct, as her evaluation processes do not reflect the rules for handling negative exponents.