To simplify the expression [tex]\( \left(2^3\right)\left[(-3-2)^0-\left(-2+3^2\right)\right] \)[/tex], follow these steps:
1. Evaluate the power of 2:
[tex]\[
2^3 = 8
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
(-3 - 2) = -5
\][/tex]
3. Evaluate the inner power:
[tex]\[
(-5)^0 = 1
\][/tex]
4. Simplify the second part inside the brackets:
[tex]\[
3^2 = 9
\][/tex]
5. Combine the terms in the second part:
[tex]\[
-2 + 9 = 7
\][/tex]
6. Combine the results within the brackets:
[tex]\[
(-5)^0 - (-2 + 3^2) = 1 - 7 = -6
\][/tex]
7. Multiply the results together:
[tex]\[
8 \times (-6) = -48
\][/tex]
Therefore, the simplified expression is:
[tex]\[
-48
\][/tex]
