To solve the expression [tex]\(\left(3 x^2\right)^0\)[/tex], we need to consider the properties of exponents.
Step-by-step solution:
1. Understand the power of zero rule:
- Any non-zero number raised to the power of 0 is always equal to 1. This is a fundamental rule in exponents.
2. Apply the rule to the given expression:
- The expression inside the parentheses is [tex]\(\left(3 x^2\right)\)[/tex].
- Irrespective of the complexities within the parentheses, as long as the base is not zero, the entire expression raised to the power of 0 simplifies to 1.
3. Check the condition:
- The condition provided is [tex]\(x \neq 0\)[/tex]. This ensures that [tex]\(3 x^2\)[/tex] is not zero because if [tex]\(x\)[/tex] were zero, [tex]\(3 x^2\)[/tex] would indeed be zero. However, since [tex]\(x \neq 0\)[/tex], [tex]\(3 x^2\)[/tex] is non-zero, and hence the rule can be applied.
4. Conclusion:
- Therefore, [tex]\(\left(3 x^2\right)^0 = 1\)[/tex].
So, the detailed step-by-step solution to the expression [tex]\(\left(3 x^2\right)^0\)[/tex] when [tex]\(x \neq 0\)[/tex] is:
[tex]\[
\boxed{1}
\][/tex]
