Question

Which expression is NOT equivalent to: (3x^4)^0 (1 point)
Responses

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

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

3x23x⋅x
3x23x⋅x

(974x^12y)^0

Answer 1

To determine which expression is NOT equivalent to \((3x^4)^0\), we first recognize that any non-zero number or expression raised to the power of 0 is equal to 1.

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

Now let's analyze each response to see if it is equivalent to 1:

1. **\(x^4 \cdot 0 \cdot x^3\)**
- This simplifies to \(0\). Since multiplying by zero gives us zero, this is NOT equivalent to 1.

2. **\(3x^2 \cdot \left(\frac{1}{3}\right)x^{-2}\)**
- The \(3\) from the first term and the \(\frac{1}{3}\) from the second term cancel out, so we have:
\[
3x^2 \cdot \frac{1}{3} x^{-2} = x^2 \cdot x^{-2} = x^{2 - 2} = x^0 = 1
\]
- This expression is equivalent to 1.

3. **\(3x^2 \cdot 3x \cdot x\)**
- This simplifies to:
\[
3x^2 \cdot 3x \cdot x = 3 \cdot 3 \cdot x^2 \cdot x^1 \cdot x^1 = 9x^{2+1+1} = 9x^4
\]
- This is NOT equivalent to 1, but it’s not the only one that fails.

4. **\((974x^{12}y)^0\)**
- This evaluates to \(1\) because any non-zero expression raised to the power of 0 equals 1.

Based on the above evaluations, the expressions **\(x^4 \cdot 0 \cdot x^3\)** and **\(3x^2 \cdot 3x \cdot x\)** are not equivalent to 1, but since the question asks for which expression is NOT equivalent to \((3x^4)^0\), the clear answer is:

**\(x^4 \cdot 0 \cdot x^3\) is NOT equivalent to \((3x^4)^0\)**.