Final answer:
The exact value of the expression 811/3 is determined by finding the cube root of 81, which involves rewriting it as 34/3 and simplifying it to give the result 4.32672.
Step-by-step explanation:
To find the exact value of the expression 811/3, we need to comprehend the concept of cubing of exponentials. Cubing involves multiplying the exponent by 3, however, in this case, we are finding the cube root, which is the inverse operation. The cube root of 81 is the number that when cubed (multiplied by itself three times) gives the product 81.
Calculation step is as follows: Since 81 is 3 to the power of 4 (34 = 81), we can rewrite 811/3 as (34)1/3. Using the property that (ab)c = abc, we can multiply the exponents to simplify this to 34/3 or 3(4/3). Now, divide 4 by 3 to get 31.333..., which equals 3 * 31/3. Since 31/3 is the cube root of 3, this simplifies to 3 multiplied by 1.44224, yielding the direct result 4.32672.