To solve the given mathematical expression [tex]\(a^3 - b^2\)[/tex] for the values [tex]\(a = -7\)[/tex] and [tex]\(b = -3\)[/tex], follow these steps:
1. Calculate [tex]\(a^3\)[/tex]:
- Given [tex]\(a = -7\)[/tex], we need to find [tex]\((-7)^3\)[/tex].
- When we cube [tex]\(-7\)[/tex], we get:
[tex]\[
(-7) \times (-7) \times (-7) = -343
\][/tex]
2. Calculate [tex]\(b^2\)[/tex]:
- Given [tex]\(b = -3\)[/tex], we need to find [tex]\((-3)^2\)[/tex].
- When we square [tex]\(-3\)[/tex], we get:
[tex]\[
(-3) \times (-3) = 9
\][/tex]
3. Subtract [tex]\(b^2\)[/tex] from [tex]\(a^3\)[/tex]:
- Now, we need to compute [tex]\(a^3 - b^2\)[/tex]:
[tex]\[
-343 - 9 = -352
\][/tex]
Thus, the value of the expression [tex]\(a^3 - b^2\)[/tex] when [tex]\(a = -7\)[/tex] and [tex]\(b = -3\)[/tex] is [tex]\(-352\)[/tex].
So, the correct answer is:
[tex]\[
\boxed{-352}
\][/tex]
