To evaluate the expression [tex]\(2^3 \cdot 3^2 \cdot 4^0\)[/tex]:
1. Evaluate each power separately:
- [tex]\(2^3\)[/tex] means [tex]\(2\)[/tex] raised to the power of [tex]\(3\)[/tex], which equals [tex]\(8\)[/tex].
- [tex]\(3^2\)[/tex] means [tex]\(3\)[/tex] raised to the power of [tex]\(2\)[/tex], which equals [tex]\(9\)[/tex].
- [tex]\(4^0\)[/tex] means [tex]\(4\)[/tex] raised to the power of [tex]\(0\)[/tex], and any number raised to the power of [tex]\(0\)[/tex] is [tex]\(1\)[/tex].
2. Multiply the results:
[tex]\[
2^3 = 8
\][/tex]
[tex]\[
3^2 = 9
\][/tex]
[tex]\[
4^0 = 1
\][/tex]
So the expression [tex]\(2^3 \cdot 3^2 \cdot 4^0\)[/tex] becomes:
[tex]\[
8 \cdot 9 \cdot 1
\][/tex]
3. Perform the multiplication:
[tex]\[
8 \cdot 9 = 72
\][/tex]
[tex]\[
72 \cdot 1 = 72
\][/tex]
4. The value of the expression [tex]\(2^3 \cdot 3^2 \cdot 4^0\)[/tex] is [tex]\(72\)[/tex].
Regarding the expression [tex]\(24^5\)[/tex]:
It is stated but not part of the operation leading to potential answers 0, 288, and 72. For clarity, focusing only on evaluating [tex]\(2^3 \cdot 3^2 \cdot 4^0\)[/tex], the final result is [tex]\(72\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{72}
\][/tex]
