Final answer:
The exact value of 27^(2/3) * (25 - 1/2) is found by first calculating the cube root of 27, squaring it to get 9, and then multiplying by (25 - 1/2), which simplifies to 24.5, resulting in the final answer of 220.5.
Step-by-step explanation:
The exact value of the expression 27^(2/3) * (25 - 1/2) can be calculated by solving each part of the expression separately and then multiplying the results.
First, we calculate the cube root of 27 and then square it, because 27 to the power of (2/3) means the cube root of 27 to the power of 2:
- 27^(1/3) = 3 (since 3^3 = 27)
- (27^(1/3))^2 = 3^2 = 9
Secondly, we calculate the value within the parentheses (25 - 1/2):
Finally, we multiply the two results together:
The exact value of the expression 27^(2/3) * (25 - 1/2) is 220.5.