Final answer:
To calculate (4 1/3)^3, convert the mixed number to an improper fraction (13/3), and then cube it to get 81.37, which is not exactly reflected in the provided options. The closest given option is 82.4 (Option a), although it does not match the calculation precisely.
Step-by-step explanation:
To calculate the value of (4 1/3)^3, we must first convert the mixed number to an improper fraction. The mixed number 4 1/3 is equivalent to (4 × 3 + 1)/3, or 13/3. Now let's compute its cube:
- (13/3)^3 = 13^3 / 3^3
- = 2197 / 27
- = 81.37037037037037 (rounded to two significant figures, 81.37)
However, the closest option to our result is 82.4 (Option a), which means there might be a rounding or calculation error in the provided options, as none of them match the calculated value exactly.
If there was any misunderstanding or different intended interpretation of the original question, none of the provided options reflect the proper calculation of (4 1/3)^3.