Simplify. 32. $9+\left[4-(10-9)^2\right]^3$

Evaluate the innermost parentheses: ( 10 − 9 ) = 1 .
Evaluate the exponent: 1 2 = 1 .
Simplify the expression inside the square brackets: [ 4 − 1 ] = 3 .
Evaluate the cube: 3 3 = 27 .
Add 9 to the result: 9 + 27 = 36 .

The simplified expression is 36 ​ .
Explanation

Understanding the Expression We are asked to simplify the expression 9 + [ 4 − ( 10 − 9 ) 2 ] 3 . To do this, we will follow the order of operations (PEMDAS/BODMAS).

Simplifying Innermost Parentheses First, we simplify the expression inside the innermost parentheses: ( 10 − 9 ) = 1 .

Evaluating the Exponent Next, we evaluate the exponent: ( 10 − 9 ) 2 = 1 2 = 1 .

Simplifying Square Brackets Now, we simplify the expression inside the square brackets: [ 4 − ( 10 − 9 ) 2 ] = [ 4 − 1 ] = 3 .

Evaluating the Cube Then, we evaluate the cube: [ 4 − ( 10 − 9 ) 2 ] 3 = 3 3 = 27 .

Adding 9 Finally, we add 9 to the result: 9 + [ 4 − ( 10 − 9 ) 2 ] 3 = 9 + 27 = 36 .


Examples
Understanding order of operations is crucial in many fields, such as computer programming, engineering, and finance. For example, when writing code, the order in which operations are performed can significantly affect the outcome of a calculation. In engineering, complex calculations often require a specific order to ensure accuracy. In finance, understanding the order of operations is essential for calculating returns on investments or managing budgets effectively.

Answered by GinnyAnswer | 2025-07-04

By following the order of operations, we simplified the expression 9 + [ 4 − ( 10 − 9 ) 2 ] 3 to find that it equals 36. We began by calculating the innermost parentheses, then squared the result, and simplified further until arriving at the final result. The entire process yielded a final answer of \boxed{36}.
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Answered by Anonymous | 2025-08-20