Absolutely, let's break this down step by step.
We start with the given expression:
[tex]\[ 16 \{ 12 + [ 25 \cdot 2 + ( 56 - 74 ) ] - [ 54 ( 12 \cdot -7 ) ] \} \][/tex]
### Step-by-Step Solution:
1. Evaluate the innermost parentheses first:
- [tex]\( 25 \cdot 2 = 50 \)[/tex]
- [tex]\( 56 - 74 = -18 \)[/tex]
- [tex]\( 12 \cdot -7 = -84 \)[/tex]
So now our expression looks like:
[tex]\[ 16 \{ 12 + [ 50 + (-18) ] - [ 54 \cdot -84 ] \} \][/tex]
2. Replace values in the expression:
- Inside the first bracket: [tex]\( 50 + (-18) = 50 - 18 = 32 \)[/tex]
- Evaluate the multiplication in the second set of brackets: [tex]\( 54 \cdot -84 = -4536 \)[/tex]
Now the expression simplifies to:
[tex]\[ 16 \{ 12 + 32 - (-4536) \} \][/tex]
3. Clear up the double negative in the middle layer:
- [tex]\( 12 + 32 + 4536 \)[/tex]
4. Add the values inside the braces:
- [tex]\( 12 + 32 = 44 \)[/tex]
- [tex]\( 44 + 4536 = 4580 \)[/tex]
Now we have:
[tex]\[ 16 \cdot 4580 \][/tex]
5. Finally, perform the multiplication:
- [tex]\( 16 \cdot 4580 = 73280 \)[/tex]
So, the result of the expression [tex]\( 16 \{ 12 + [ 25 \cdot 2 + ( 56 - 74 ) ] - [ 54 ( 12 \cdot -7 ) ] \} \)[/tex] is:
[tex]\[
73280
\][/tex]
