To solve the expression [tex]\( a^3 - b^2 \)[/tex] for [tex]\( a = -7 \)[/tex] and [tex]\( b = -3 \)[/tex], we'll follow these steps:
1. Calculate [tex]\( a^3 \)[/tex]:
[tex]\[
a^3 = (-7)^3
\][/tex]
Raising [tex]\(-7\)[/tex] to the third power:
[tex]\[
(-7) \times (-7) \times (-7) = -343
\][/tex]
So, [tex]\( a^3 = -343 \)[/tex].
2. Calculate [tex]\( b^2 \)[/tex]:
[tex]\[
b^2 = (-3)^2
\][/tex]
Squaring [tex]\(-3\)[/tex]:
[tex]\[
(-3) \times (-3) = 9
\][/tex]
So, [tex]\( b^2 = 9 \)[/tex].
3. Substitute these values into the expression [tex]\( a^3 - b^2 \)[/tex]:
[tex]\[
a^3 - b^2 = -343 - 9
\][/tex]
4. Perform the subtraction:
[tex]\[
-343 - 9 = -352
\][/tex]
Therefore, 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]. The correct answer is:
D. [tex]\(-352\)[/tex]
