Final answer:
To evaluate the expression 17 - {2 + 2[-1(7 - 10)]^2}, first solve the expression within the brackets, then perform exponentiation, and finally subtract the result from 17. The value of the expression is -19.
Step-by-step explanation:
To evaluate the expression 17 - {2 + 2[-1(7 - 10)]^2}, we need to follow the order of operations, which states that we should solve any operations within parentheses first, followed by exponentiation, multiplication and division from left to right, and finally addition and subtraction from left to right.
First, let's solve the expression within the brackets: 7 - 10 = -3. Next, we multiply -3 by -1, which gives us 3. Then, we multiply 3 by 2, resulting in 6. So, the expression within the brackets simplifies to 6.
Now, we can solve the exponentiation: 6^2 = 36.
Finally, we can perform the subtraction: 17 - 36 = -19.
Therefore, the value of the expression 17 - {2 + 2[-1(7 - 10)]^2} is -19.