To determine the value of the expression [tex]\(a^3 - b^2\)[/tex] when [tex]\(a = -7\)[/tex] and [tex]\(b = -3\)[/tex], follow these steps:
1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[
a^3 = (-7)^3 = -7 \cdot -7 \cdot -7 = -343
\][/tex]
2. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
b^2 = (-3)^2 = (-3) \cdot (-3) = 9
\][/tex]
3. Compute the expression [tex]\(a^3 - b^2\)[/tex]:
[tex]\[
a^3 - b^2 = -343 - 9 = -352
\][/tex]
Thus, the value of the expression [tex]\(a^3 - b^2\)[/tex] is [tex]\(-352\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{-352}
\][/tex]
