To evaluate [tex]\(\left(2 y^2\right)^0\)[/tex] where [tex]\(y = 3\)[/tex], we need to follow these steps:
1. Substitute the value of [tex]\(y\)[/tex] into the expression:
Since [tex]\(y = 3\)[/tex], replace [tex]\(y\)[/tex] with 3 in the expression [tex]\((2 y^2)^0\)[/tex].
2. Simplify the expression inside the parentheses:
Calculate [tex]\(2 y^2\)[/tex] when [tex]\(y = 3\)[/tex].
[tex]\[
2 (3)^2 = 2 \cdot 9 = 18
\][/tex]
3. Evaluate the expression with the exponent:
Now we have the expression [tex]\(18^0\)[/tex].
4. Apply the zero exponent rule:
According to the mathematical rule, any number (except zero) raised to the power of 0 is 1.
Therefore, [tex]\(\left(2 y^2 \right)^0 = 1\)[/tex].
The correct value is [tex]\( \boxed{1} \)[/tex].
