Question

Which expression is NOT equivalent to: (3x^4)^0 (1 point) Responses x^4⋅0x^3 x to the 4th power times 0 x cubed 3x^2 / 3x⋅x
3x^2⋅(1/3)x^−2 3 times x squared times 1 third x to the negative 2 power (974x^12 y)^0

Answer 1

To determine which expression is NOT equivalent to \((3x^4)^0\), we need to understand that any non-zero quantity raised to the power of zero equals 1. Therefore, \((3x^4)^0 = 1\).

Now let's analyze the provided options:

1. **\(x^4 \cdot 0x^3\)**: This expression is zero because it involves multiplying by zero. Thus, it is not equivalent to 1.

2. **\(x^4\) times 0**: This also results in zero, similar to the above.

3. **\(3x^2 / 3x \cdot x\)**: Simplifying this gives \(x^2 / x^2 = 1\) (as long as \(x\) is not zero), so it is equivalent to 1.

4. **\(3x^2 \cdot (1/3)x^{-2}\)**: Simplifying gives \(3x^{2} \cdot \frac{1}{3}x^{-2} = x^{2} \cdot x^{-2} = 1\) (as long as \(x\) is not zero), making it equivalent to 1.

5. **\((974x^{12}y)^0\)**: This expression evaluates to 1, since it is also a non-zero quantity raised to the power of zero.

From this examination, the two expressions that result in zero (\(x^4 \cdot 0x^3\) and \(x^4\) times 0) are not equivalent to \((3x^4)^0\).

However, as the question asks for a single expression that is not equivalent, the simplest references would be:

**Final Answers:**
- **\(x^4 \cdot 0x^3\)** and **\(x^4\) times 0** are both NOT equivalent to \( (3x^4)^0\).

If needed to pick just one to align with the format:

- **\(x^4 \cdot 0x^3\)** is a valid single response that is NOT equivalent to \((3x^4)^0\).