Let's solve the given expression step-by-step.
Given mathematical expression is:
[tex]\[
(-12) \left\{ 45 + 6(-12) - \left[ -3 \times (6 + 9) \right] \times \left[ 24 - (-5) \times (-4) \right] \right\}
\][/tex]
### Step 1: Calculate the innermost expression
Firstly, calculate the product inside the innermost brackets:
[tex]\[
(-5) \times (-4) = 20
\][/tex]
### Step 2: Evaluate the expression inside the square brackets
Now substitute [tex]\( 20 \)[/tex] back into the square brackets:
[tex]\[
24 - 20 = 4
\][/tex]
This simplifies the expression inside the square brackets to [tex]\( 4 \)[/tex].
### Step 3: Calculate the next set of multiplication inside the curly braces
Calculate the product with [tex]\( 9 \)[/tex] inside the expression:
[tex]\[
9 \times 4 = 36
\][/tex]
### Step 4: Simplify the rest of the expression inside the curly braces
Substitute [tex]\( 36 \)[/tex] back into the curly braces:
[tex]\[
45 + 6(-12) - (-3) \times (6 + 9) - 36
\][/tex]
First, simplify inside the parentheses:
[tex]\[
6 + 9 = 15
\][/tex]
Then, calculate the products:
[tex]\[
6 \times (-12) = -72
\][/tex]
[tex]\[
-3 \times 15 = -45
\][/tex]
Now substitute these values back:
[tex]\[
45 + (-72) - (-45) - 36
\][/tex]
Simplify the additions and subtractions inside the curly braces:
[tex]\[
45 + (-72) = -27
\][/tex]
[tex]\[
-27 - 36 = -63
\][/tex]
[tex]\[
-63 + 45 = -18
\][/tex]
### Step 5: Multiply the result by -12
Finally, multiply the result inside the curly braces by [tex]\( -12 \)[/tex]:
[tex]\[
-12 \times -45 = 540
\][/tex]
So, the final value of the given mathematical expression is:
[tex]\[
540
\][/tex]
Thus, the result is [tex]\( 540 \)[/tex].
