Question

Which expression is NOT equivalent to: (3x4)0(3𝑥4)0(1 point)Responsesx4⋅0x3𝑥4⋅0𝑥3x to the 4th power times 0 x cubed3x23x⋅x3𝑥23𝑥⋅𝑥3x23x⋅x3𝑥23𝑥⋅𝑥3x2⋅(13)x−23𝑥2⋅(13)𝑥−23 times x squared times 1 third x to the negative 2 power(974x12y)0

Answer 1

The expression \((3x^4)^0(3x^4)^0\) simplifies to \(1 \cdot 1 = 1\) because any nonzero expression raised to the power of 0 equals 1.

Now, let's analyze each response to find which one is NOT equivalent to 1.

1. \(x^4 \cdot 0\): This equals \(0\) since anything times \(0\) is \(0\).
2. \(x^3 \cdot 0\): This also equals \(0\).
3. \(3x^2\): This expression is variable-dependent and will not equal \(1\) for all \(x\).
4. \(3x \cdot x^3\): This equals \(3x^4\), which is variable-dependent and not equal to \(1\) for all \(x\).

To summarize the responses:
- The first two are clearly not equivalent because they yield \(0\).
- The expressions \(3x^2\) and \(3x \cdot x^3\) yield values dependent on \(x\), which could never equal \(1\) for all \(x\).

However, the direct answer you are looking for, which is the expression that is NOT equivalent to \( (3x^4)^0(3x^4)^0 \) = \(1\), includes any expression that results in \(0\) or is dependent on a variable.

So the final answer would be \(x^4 \cdot 0\) or \(x^3 \cdot 0\), since both yield \(0\), which is NOT equivalent to \(1\). Therefore, the answer is:

**\(x^4 \cdot 0\)**