Let's solve the expression step-by-step:
1. Calculate [tex]\((-2)^3\)[/tex]:
[tex]\[
(-2)^3 = (-2) \times (-2) \times (-2)
\][/tex]
First, [tex]\((-2) \times (-2)\)[/tex] equals [tex]\(4\)[/tex].
Then, [tex]\(4 \times (-2)\)[/tex] equals [tex]\(-8\)[/tex].
So, [tex]\((-2)^3 = -8\)[/tex].
2. Calculate [tex]\((-3)^2\)[/tex]:
[tex]\[
(-3)^2 = (-3) \times (-3)
\][/tex]
[tex]\((-3) \times (-3)\)[/tex] equals [tex]\(9\)[/tex].
So, [tex]\((-3)^2 = 9\)[/tex].
3. Sum the results:
[tex]\[
-8 + 9
\][/tex]
Adding these together, [tex]\(-8 + 9\)[/tex] equals [tex]\(1\)[/tex].
Thus, the value of the expression [tex]\((-2)^3 + (-3)^2\)[/tex] is [tex]\(\boxed{1}\)[/tex].
