Let's simplify the expression [tex]\(\left(p^2 + 3\right)^0\)[/tex].
### Step-by-Step Solution:
1. Understanding the Zero Exponent Rule:
According to the properties of exponents, any non-zero number raised to the power of 0 is equal to 1. This rule is stated mathematically as:
[tex]\[
a^0 = 1 \quad \text{for any } a \neq 0.
\][/tex]
2. Analyze the Base:
In the given expression, the base is [tex]\(p^2 + 3\)[/tex]. Notice that [tex]\(p^2 + 3\)[/tex] is always non-zero because:
[tex]\[
p^2 \quad \text{(square of any real number)} \quad \geq 0, \quad \text{and adding 3 makes it strictly positive}.
\][/tex]
Hence, [tex]\(p^2 + 3\)[/tex] cannot be zero for any real number [tex]\(p\)[/tex].
3. Applying the Zero Exponent Rule:
Since [tex]\(p^2 + 3\)[/tex] is always a non-zero positive number, we apply the zero exponent rule:
[tex]\[
\left(p^2 + 3\right)^0 = 1.
\][/tex]
Therefore, the simplified result of [tex]\(\left(p^2 + 3\right)^0\)[/tex] is:
[tex]\[
1
\][/tex]
### Final Answer:
[tex]\[
\left(p^2 + 3\right)^0 = 1.
\][/tex]
