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We are asked to evaluate the expression $90 - 5\{10-[3^2 - 2(12-8)]\}$.

ArithmeticOrder of OperationsExponentsArithmetic Expressions
2025/5/15

1. Problem Description

We are asked to evaluate the expression 90−5{10−[32−2(12−8)]}90 - 5\{10-[3^2 - 2(12-8)]\}.

2. Solution Steps

First, we simplify the innermost parentheses:
12−8=412 - 8 = 4
The expression becomes 90−5{10−[32−2(4)]}90 - 5\{10-[3^2 - 2(4)]\}.
Next, we evaluate the exponent:
32=93^2 = 9
The expression becomes 90−5{10−[9−2(4)]}90 - 5\{10-[9 - 2(4)]\}.
Now, we evaluate the multiplication inside the square brackets:
2(4)=82(4) = 8
The expression becomes 90−5{10−[9−8]}90 - 5\{10-[9 - 8]\}.
Next, we simplify the expression inside the square brackets:
9−8=19 - 8 = 1
The expression becomes 90−5{10−1}90 - 5\{10-1\}.
Now, we simplify the expression inside the curly braces:
10−1=910 - 1 = 9
The expression becomes 90−5{9}90 - 5\{9\}.
Next, we evaluate the multiplication:
5{9}=5(9)=455\{9\} = 5(9) = 45
The expression becomes 90−4590 - 45.
Finally, we perform the subtraction:
90−45=4590 - 45 = 45

3. Final Answer

45

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