Final answer:
To find the value of 6 2/3 raised to the third power, convert to a fraction (20/3), then cube the numerator and denominator to get 8000/27, which is approximately 296.2963.
Step-by-step explanation:
The question involves calculating the value of 6 2/3 raised to the third power. To solve this, first convert 6 2/3 to an improper fraction. 6 2/3 is the same as 20/3 since 6 * 3 + 2 = 20. Now, we need to raise 20/3 to the third power:
- Write the expression as (20/3)³.
- Cube both the numerator and denominator separately: 20³ = 8000 and 3³ = 27.
- Write the final answer as 8000/27.
Therefore, 6 2/3 raised to the third power is 8000/27, which is approximately 296.2963