First, we need to evaluate the expression [tex]\(\left(-3 g^2\right)^0\)[/tex] where [tex]\(g = 0\)[/tex].
1. Substitute [tex]\(g = 0\)[/tex] into the given expression:
[tex]\[
(-3 g^2)^0
\][/tex]
2. Calculate [tex]\(g^2\)[/tex] where [tex]\(g = 0\)[/tex]:
[tex]\[
g^2 = 0^2 = 0
\][/tex]
3. Substitute [tex]\(g^2 = 0\)[/tex] back into the expression:
[tex]\[
(-3 \cdot 0)^0
\][/tex]
4. Perform the multiplication inside the parentheses:
[tex]\[
-3 \cdot 0 = 0
\][/tex]
5. Now the expression simplifies to:
[tex]\[
0^0
\][/tex]
6. According to mathematical conventions, the expression [tex]\(0^0\)[/tex] is typically defined as 1, though it can be debated in different contexts. However, in this case, we follow the standard convention:
[tex]\[
0^0 = 1
\][/tex]
So, the value of the expression [tex]\(\left(-3 g^2\right)^0\)[/tex] where [tex]\(g = 0\)[/tex] is [tex]\(1\)[/tex].
