Sure, let's solve the expression step-by-step:
Given expression:
[tex]\[
\left\{-10-\left[12+(-3)^2\right]+3^3\right\} \div(-3)
\][/tex]
1. Step 1: Evaluate the innermost brackets: [tex]\((-3)^2\)[/tex]:
[tex]\[
(-3)^2 = 9
\][/tex]
2. Step 2: Add 12 and 9:
[tex]\[
12 + 9 = 21
\][/tex]
3. Step 3: Substitute back into the expression and simplify the intermediate result:
[tex]\[
-10 - 21
\][/tex]
4. Step 4: Perform the subtraction:
[tex]\[
-10 - 21 = -31
\][/tex]
5. Step 5: Add [tex]\(3^3\)[/tex] which is the next term to simplify:
[tex]\[
3^3 = 27
\][/tex]
6. Step 6: Add 27 to [tex]\(-31):
\[
-31 + 27 = -4
\]
7. Step 7: Finally, divide by \(-3\)[/tex]:
[tex]\[
\frac{-4}{-3} = 1.3333333333333333
\][/tex]
So, the final result of the expression is:
[tex]\[
1.3333333333333333
\][/tex]
