To solve the expression [tex]\( \left(3x^2\right)^0 = v \)[/tex] for [tex]\( v \)[/tex], where [tex]\( x \neq 0 \)[/tex], let's proceed step by step:
1. Recognize the base and the exponent:
- The base of our expression is [tex]\( 3x^2 \)[/tex].
- The exponent is 0.
2. Apply the properties of exponents:
- According to the properties of exponents, any non-zero number raised to the power of 0 is equal to 1.
3. Confirm that the base is non-zero:
- Since [tex]\( x \neq 0 \)[/tex], [tex]\( 3x^2 \)[/tex] is also non-zero. Thus, we can safely apply the exponent property.
4. Simplify the expression:
- Given that the base [tex]\( 3x^2 \)[/tex] is non-zero, raising it to the power of 0 results in 1. Therefore, [tex]\( \left(3x^2\right)^0 = 1 \)[/tex].
Hence, the value of [tex]\( v \)[/tex] is [tex]\( 1 \)[/tex].
[tex]\[ v = 1 \][/tex]
