Question
3. \( 2^{\frac{1}{3}} \cdot 4^{\frac{1}{3}} \) a. \( \sqrt[3]{2} \) b. \( \sqrt{2} \) c. 4 d. 2
Ask by Warren Lee. in the United States
Dec 03,2024
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression simplifies to 2. Therefore, the correct answer is d. 2.
Solution
Calculate or simplify the expression \( 2^(1/3) * 4^(1/3) \).
Calculate the value by following steps:
- step0: Calculate:
\(2^{\frac{1}{3}}\times 4^{\frac{1}{3}}\)
- step1: Rewrite the expression:
\(2^{\frac{1}{3}}\times 2^{\frac{2}{3}}\)
- step2: Simplify:
\(2\)
The expression \(2^{\frac{1}{3}} \cdot 4^{\frac{1}{3}}\) simplifies to 2.
Therefore, the correct answer is d. 2.
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Simplify this solution The Deep Dive
To simplify \( 2^{\frac{1}{3}} \cdot 4^{\frac{1}{3}} \), we first rewrite 4 as \( 2^2 \). This gives us: \[ 2^{\frac{1}{3}} \cdot (2^2)^{\frac{1}{3}} = 2^{\frac{1}{3}} \cdot 2^{\frac{2}{3}} = 2^{\frac{1}{3} + \frac{2}{3}} = 2^{1} = 2 \] So, the answer is d. 2! Now you can impress your friends with your mastery of exponents!
