Question

Which expression is NOT equivalent to: (3x4)0
(1 point)
Responses

3x23x⋅x
3x23x⋅x

x4⋅0x3
x to the 4th power times 0 x cubed

(974x12y)0
open paren 974 x to the 12th power y close paren to the 0 power

3x2⋅(13)x−2

Answer 1

To determine which expression is NOT equivalent to \((3x^4)^0\), we need to understand that any expression raised to the power of 0 is equal to 1, provided the base is not zero.

Thus, \((3x^4)^0 = 1\).

Now let's evaluate each of the provided options:

1. **\(3x^2 \cdot 3x \cdot x\)**:
- This simplifies to \(3x^4\), which is NOT equal to 1.

2. **\(x^4 \cdot 0 \cdot x^3\)**:
- This expression equals 0, not equal to 1.

3. **\((974x^{12}y)^0\)**:
- This equals 1, since any non-zero expression raised to the power of 0 is 1.

4. **\(3x^2 \cdot (13)x^{-2}\)**:
- This simplifies to \(3 \cdot 13 \cdot x^0\), which equals \(39\) (since \(x^0 = 1\)), which is NOT equal to 1.

Based on this analysis, the expressions that are NOT equivalent to \((3x^4)^0\) are:

- \(3x^2 \cdot 3x \cdot x\) (simplifies to \(3x^4\))
- \(x^4 \cdot 0 \cdot x^3\) (equals 0)
- \(3x^2 \cdot (13)x^{-2}\) (simplifies to 39)

However, since the question asks for one that is NOT equivalent, the bold answers are:

**Responses:**
- \(3x^2 \cdot 3x \cdot x\)
- \(x^4 \cdot 0 \cdot x^3\)
- \(3x^2 \cdot (13)x^{-2}\)

The easiest and clearest answer to choose from the provided options that is NOT equivalent to \((3x^4)^0\) would be \(x^4 \cdot 0 \cdot x^3\), as that directly equals 0.