Final answer:
The simplified value of the expression (7-2)^2 + (6-2)^3 is calculated by first solving the expressions in parentheses, then applying the exponents, and finally adding the results together to get 89.
Step-by-step explanation:
To find the simplified value of the expression (7-2)^2 + (6-2)^3, we need to perform the operations step by step, following the order of operations known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
First, we calculate the value inside the parentheses:
- (7-2) gives us 5
- (6-2) gives us 4
Next, we raise these values to the power given:
- 5 squared, or 5^2, is 25
- 4 cubed, or 4^3, is 64
Finally, we add these two results together:
25 + 64 = 89
Therefore, the simplified value of the expression is 89, which corresponds to option D.