| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B |
B |
| deepseekr1 | To simplify \((x\sqrt{x^3})^4\), start by rewriting the square root as an exponent: \(\sqrt{x^3} = x^{3/2}\). The expression inside the parentheses becomes \(x \cdot x^{3/2}\). When multiplying terms with the same base, add the exponents: \(1 + \frac{3}{2} = \frac{5}{2}\), resulting in \(x^{5/2}\). Next, raise \(x^{5/2}\) to the 4th power: \((x^{5/2})^4\). Multiply the exponents: \(\frac{5}{2} \times 4 = 10\). Therefore, the exponent of \(x\) is **10**. **Answer: B** |
B |
| gpto1 | B | B |
| GPT-4o | To simplify \((x\sqrt{x^3})^4\), let's break it down step by step. First, consider the expression inside the parentheses: \(x\sqrt{x^3}\). Recall that \(\sqrt{x^3} = x^{3/2}\). So, we can rewrite the expression as: \[ x \cdot x^{3/2} \] Using the properties of exponents, we add the exponents: \[ x^{1 + 3/2} = x^{2.5} = x^{5/2} \] Now, we raise this to the fourth power: \[ (x^{5/2})^4 \] Using the property of exponents \((a^m)^n = a^{m \cdot n}\), we get: \[ x^{(5/2) \cdot 4} = x^{10} \] So, the exponent of \(x\) in the simplified expression is 10. Therefore, the correct answer is: \[ \boxed{B} \] |
B |
| llama3.1-70B-Instruct | D |
B |
| llama3.1-405B-Instruct | B |
B |
| DeepSeek-Coder-V2 | D. 12 | B |
| Qwen2-72B-Instruct | D. 12 | B |
| baichuan4 | B | B |
| doubao | \[ \begin{align*} &(x\sqrt{x^3})^4\\ =&(x\cdot x^{\frac{3}{2}})^4\\ =&(x^{\frac{5}{2}})^4\\ =&x^{(\frac{5}{2})\times4}\\ =&x^{10} \end{align*} \] So the answer is B. |
B |
| minimax | To simplify $(x\sqrt{x^3})^4$, we first need to simplify the expression inside the parentheses. The square root of $x^3$ can be written as $x^{3/2}$. So the expression becomes: $(x \cdot x^{3/2})^4$ Now, when we multiply powers with the same base, we add the exponents: $x^1 \cdot x^{3/2} = x^{1 + 3/2} = x^{5/2}$ Now we raise this to the 4th power: $(x^{5/2})^4$ When we raise a power to a power, we multiply the exponents: $x^{5/2 \cdot 4} = x^{10}$ So the exponent of $x$ when $(x\sqrt{x^3})^4$ is simplified is 10. The correct answer is: B. 10 |
B |
| kimi | To solve this problem, we can simplify the expression step by step: 1. First, recognize that $\sqrt{x^3}$ is the same as $x^{3/2}$ because the square root is the same as raising to the power of $1/2$. 2. Now, we have $(x \cdot x^{3/2})^4$. 3. When multiplying powers with the same base, we add the exponents, so $x \cdot x^{3/2} = x^{1 + 3/2} = x^{5/2}$. 4. Raising this to the power of 4, we multiply the exponents: $(x^{5/2})^4 = x^{(5/2) \cdot 4} = x^{10}$. So the exponent of $x$ in the simplified expression is 10. Answer: B. 10 |
B |
| wenxinyiyan | D Explanation: $(x\sqrt{x^3})^4$ = $(x \cdot x^{\frac{3}{2}})^4$ (since $\sqrt{x^3}$ can be written as $x^{\frac{3}{2}}$) = $(x^{1+\frac{3}{2}})^4$ (using the law of exponents: $a^m \cdot a^n = a^{m+n}$) = $(x^{\frac{5}{2}})^4$ (simplifying the exponent) = $x^{\frac{5}{2} \times 4}$ (using the law of exponents: $(a^m)^n = a^{m \times n}$) = $x^{10}$ (simplifying the exponent) So, the exponent of $x$ is 10, but since the question asks for the exponent in $(x\sqrt{x^3})^4$ which is already raised to the power of 4, the actual exponent in the original expression is $\frac{10}{4} = 2.5$. However, we need to consider the expression as it is, i.e., after simplifying the square root but before distributing the outer exponent. Thus, the exponent in $(x\sqrt{x^3})$ is $1 + \frac{3}{2} = \frac{5}{2}$ and when this is multiplied by 4 (the outer exponent), we get 10. Since the options are provided for the exponent after applying the outer exponent, the answer is 10 corresponding to option B. Note: There is a possibility of confusion in the question. If the question means to ask the exponent of the simplified form of $(x\sqrt{x^3})^4$, then the answer is 10 (option B). But if the question means to ask the exponent within the parentheses $(x\sqrt{x^3})$ before applying the outer exponent of 4, then the answer would be $\frac{5}{2}$ or 2.5, which is not given as an option. Assuming the former case, the provided answer is B. However, upon rereading the question, it seems to ask for the final exponent after fully simplifying $(x\sqrt{x^3})^4$. In this case, the final exponent is indeed 10, making B the correct answer. Edit: Clarified the explanation to match the correct interpretation of the question. The final exponent after simplifying is 10, so the answer is B. The initial confusion arose from interpreting the question as asking for the exponent within the parentheses before applying the outer exponent, which is not the case. |
B |
| zhipu | To simplify \((x\sqrt{x^3})^4\), let's break down the expression step by step. First, recall that the square root of \(x^3\) can be written as \((x^3)^{1/2}\). So, the expression becomes: \[ x \cdot (x^3)^{1/2} \] Next, apply the power rule \((a^m)^n = a^{mn}\): \[ (x \cdot (x^3)^{1/2})^4 \] Now, distribute the exponent \(4\) to both parts inside the parentheses: \[ x^4 \cdot ((x^3)^{1/2})^4 \] Simplify \((x^3)^{1/2}\): \[ (x^3)^{1/2} = x^{3/2} \] Then raise \(x^{3/2}\) to the power of \(4\): \[ (x^{3/2})^4 = x^{(3/2) \cdot 4} = x^6 \] Now, combine the exponents: \[ x^4 \cdot x^6 = x^{4+6} = x^{10} \] Therefore, the exponent of \(x\) is \(10\). The correct answer is: B. 10 |
B |
| gpto1 | B | B |
| deepseekv3 | To simplify \((x\sqrt{x^3})^4\) and find the exponent of \(x\), follow these steps: 1. **Simplify the expression inside the parentheses:** \[ \sqrt{x^3} = x^{3/2} \] So, \[ x\sqrt{x^3} = x \cdot x^{3/2} = x^{1 + 3/2} = x^{5/2} \] 2. **Raise the simplified expression to the 4th power:** \[ (x^{5/2})^4 = x^{(5/2) \cdot 4} = x^{10} \] Thus, the exponent of \(x\) in the simplified expression is **10**. **Answer:** \(\boxed{B}\) |
B |