Question

Which expression is NOT equivalent to: (3x^4)^0 (1 point) A. x^4 x 0x^3. B. 3x^2 x (1/3) x^-2 C. 3x^2/ 3x times x D. (974x^12y)^0

Answer 1

To analyze which expression is NOT equivalent to \((3x^4)^0\), we first note 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 evaluate each option:

A. \(x^4 \cdot 0x^3\)
This expression simplifies to \(0\) (since \(0 \times x^3 = 0\)). Thus, it is NOT equivalent to 1.

B. \(3x^2 \cdot (1/3) \cdot x^{-2}\)
This can be simplified:
\[
3x^2 \cdot (1/3) = x^2
\]
\[
x^2 \cdot x^{-2} = x^{2 - 2} = x^0 = 1
\]
This is equivalent to 1.

C. \(\frac{3x^2}{3x} \cdot x\)
This simplifies as follows:
\[
\frac{3x^2}{3x} = x \quad(\text{since } 3 \text{ cancels out})
\]
\[
x \cdot x = x^{1 + 1} = x^2
\]
This is not equal to 1.

D. \((974x^{12}y)^0\)
This is equal to 1, since it is also raised to the power of 0.

From the evaluations, the expressions that are NOT equivalent to \((3x^4)^0\) are A and C, but since we need to identify just one option, the correct answer is:

**A. \(x^4 \cdot 0x^3\)**