Question
Evaluate. \( \frac{2}{3} \sqrt{81}-\sqrt[3]{-27}-\frac{4}{3} \sqrt[3]{729} \) -3 -9
Ask by Wells Love. in the United States
Feb 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The value of the expression is -3.
Solution
We begin by computing each term step by step.
1. √81 = 9. Multiplying by 2/3, we have (2/3) × 9 = 6.
2. The cube root of -27 is -3, since (-3)³ = -27.
3. The cube root of 729 is 9, because 9³ = 729. Multiplying by 4/3 gives (4/3) × 9 = 12.
Now substitute these back into the expression:
6 - (-3) - 12 = 6 + 3 - 12 = -3.
Thus, the value of the expression is -3.
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Simplify this solution Extra Insights
Let's evaluate the expression step by step. First, we calculate each term separately: 1. \( \frac{2}{3} \sqrt{81} \) Since \( \sqrt{81} = 9 \), we have: \( \frac{2}{3} \times 9 = 6 \). 2. \( \sqrt[3]{-27} \) The cube root of -27 is -3, so: \( \sqrt[3]{-27} = -3 \). 3. \( \frac{4}{3} \sqrt[3]{729} \) The cube root of 729 is 9, so: \( \frac{4}{3} \times 9 = 12 \). Now, we can combine these results into the original expression: \[ 6 - (-3) - 12 \] This simplifies to: \[ 6 + 3 - 12 = 9 - 12 = -3. \] Therefore, the answer is \(-3\).
