To solve the expression [tex]\(a^3 - b^2\)[/tex] given that [tex]\(a = -7\)[/tex] and [tex]\(b = -3\)[/tex], follow these steps:
1. Calculate [tex]\(a^3\)[/tex]:
[tex]\[
a = -7
\][/tex]
[tex]\[
a^3 = (-7)^3
\][/tex]
[tex]\[
(-7)^3 = -7 \times -7 \times -7
\][/tex]
[tex]\[
= -343
\][/tex]
2. Calculate [tex]\(b^2\)[/tex]:
[tex]\[
b = -3
\][/tex]
[tex]\[
b^2 = (-3)^2
\][/tex]
[tex]\[
(-3)^2 = -3 \times -3
\][/tex]
[tex]\[
= 9
\][/tex]
3. Combine the results to find [tex]\(a^3 - b^2\)[/tex]:
[tex]\[
a^3 - b^2 = -343 - 9
\][/tex]
[tex]\[
= -352
\][/tex]
Therefore, the correct value of the expression [tex]\(a^3 - b^2\)[/tex] is [tex]\( -352 \)[/tex].
The correct answer is:
B. -352
