15-[8³+3²-{8²-(42+2³)-5³}-2²]
15-[8³+3²-{8²-(42+2³)-5³}-2²]
keep nibbling away at it from the inside
= 15-[8³+3²-{8²-(50)-5³}-2²]
= 15-[8³+3²-{-111}-2²
= 15-[8³+3²+111-2²]
= 15-[512 + 9 + 111 - 4]
= 15 - 628
= -613
To simplify the expression 15 - [8³ + 3² - {8² - (42 + 2³) - 5³} - 2²], let's break down the steps:
Step 1: Start by solving the innermost parentheses.
Inside the curly braces: (42 + 2³) = (42 + 8) = 50.
Step 2: Simplify further within the innermost parentheses.
Inside the square brackets: 8² - 50 - 5³ = 64 - 50 - 125 = -111.
Step 3: Continue with the other operations.
Inside the square brackets: 8³ + 3² - (-111) - 2²
= 512 + 9 + 111 - 4
= 632.
Step 4: Evaluate the expression.
15 - 632
= -617.
So, 15 - [8³ + 3² - {8² - (42 + 2³) - 5³} - 2²] simplifies to -617.
To simplify the expression 15 - [8³ + 3² - {8² - (42 + 2³) - 5³} - 2²], let's break it down step by step:
1. Start by simplifying the innermost parentheses:
42 + 2³ = 42 + 8 = 50
2. Now, continue simplifying the expression within the curly brackets:
8² - 50 - 5³ = 64 - 50 - 125 = -111
3. Next, simplify the expression within the square brackets:
8³ + 3² - (-111) - 2²
To evaluate this, raise each number to its designated power:
8³ = 8 * 8 * 8 = 512
3² = 3 * 3 = 9
Now we can substitute these values back into the expression:
512 + 9 - (-111) - 4
Simplify the double negatives: -(-111) becomes +111
512 + 9 + 111 - 4
4. Combine like terms:
512 + 9 + 111 - 4 = 632
5. Finally, substitute this result back into the original expression:
15 - [632] = 15 - 632
6. Now, subtract:
15 - 632 = -617
Therefore, the simplified result of the expression 15 - [8³ + 3² - {8² - (42 + 2³) - 5³} - 2²] is -617.