Question

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

3x2⋅(13)x−2
3 times x squared times 1 third x to the negative 2 power

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

3x23x⋅x
3x23x⋅x

(974x12y)0

Answer 1

To determine which expression is NOT equivalent to \( (3x^4)^0 \), we can evaluate each option.

1. **Evaluate \( (3x^4)^0 \)**:
According to the property of exponents, any non-zero expression raised to the power of 0 equals 1. Hence, \( (3x^4)^0 = 1 \).

Now let’s evaluate or simplify each of the given options:

1. **Option 1**: \( 3x^2 \cdot (1/3)x^{-2} \)
- Simplifying gives: \( 3x^2 \cdot \frac{1}{3} \cdot \frac{1}{x^2} = 1 \) (the 3s cancel out, and \( x^2/x^2 = 1 \))

2. **Option 2**: \( x^4 \cdot 0 \cdot x^3 \)
- Simplifying gives: \( 0 \) (anything multiplied by 0 is 0)

3. **Option 3**: \( 3x^2 \cdot 3x \cdot x \)
- Simplifying gives: \( 3^2 \cdot x^2 \cdot x^2 = 9x^4 \) (which is not equal to 1)

4. **Option 4**: \( (974x^{12}y)^0 \)
- Simplifying gives: \( 1 \) (same as before, any non-zero expression raised to the power of 0 equals 1)

After evaluating all the options, we find:

- Options 1, 4 yield 1.
- Option 2 yields 0.
- Option 3 yields \( 9x^4 \).

The expression that is NOT equivalent to \( (3x^4)^0 \) is therefore:

**Option 2**: \( x^4 \cdot 0 \cdot x^3 \) (since it equals 0), and **Option 3**: \( 3x^2 \cdot 3x \cdot x \) (since it equals \( 9x^4 \)) are both non-equivalent. However, Option 2 is more clear cut as it equals exactly 0.

Thus, the final answer is:

**Response**: Option 2: \( x^4 \cdot 0 \cdot x^3 \)