Let's simplify the expression \( 78 - [24 - 516[5 - 4 - 6]] \) step-by-step.
1. Simplify the innermost expression first:
[tex]\[
5 - 4 - 6
\][/tex]
Compute \( 5 - 4 \):
[tex]\[
5 - 4 = 1
\][/tex]
Then, subtract 6 from 1:
[tex]\[
1 - 6 = -5
\][/tex]
2. Replace the innermost expression with its result:
[tex]\[
78 - [24 - 516 \times (-5)]
\][/tex]
3. Next, multiply \( 516 \) by \(-5\):
[tex]\[
516 \times (-5) = -2580
\][/tex]
4. Substitute \(-2580\) into the expression:
[tex]\[
78 - [24 - (-2580)]
\][/tex]
5. Simplify the expression inside the brackets:
[tex]\[
24 - (-2580) = 24 + 2580 = 2604
\][/tex]
6. Finally, subtract 2604 from 78:
[tex]\[
78 - 2604 = -2526
\][/tex]
So, the simplified result of the expression is:
[tex]\[
-2526
\][/tex]
