Question

Which expression is NOT equivalent to: (3x to the fourth power) to the zero power

3x to the second power times (1/2)x to the negative second power
x to the fourth power times 0x to the third power
3x to the second power divided by 3x times x
(974x to the twelfth power y) to the zero power

Answer 1

Let's analyze the expression \((3x^4)^0\).

According to the zero exponent rule, any non-zero number raised to the zero power is equal to 1. Thus:

\[
(3x^4)^0 = 1
\]

Now we will check each of the provided expressions to see which one is NOT equivalent to 1.

1. **Expression A**: \(3x^2 \cdot \left(\frac{1}{2}\right)x^{-2}\)
\[
= \frac{3}{2} x^{2 - 2} = \frac{3}{2} x^0 = \frac{3}{2} \cdot 1 = \frac{3}{2}
\]
This expression is NOT equal to 1.

2. **Expression B**: \(x^4 \cdot 0x^3\)
\[
= 0 \cdot x^4 = 0
\]
This expression is NOT equal to 1.

3. **Expression C**: \(\frac{3x^2}{3x} \cdot x\)
\[
= x \cdot x = x^2
\]
This expression is NOT equal to 1 unless \(x = 1\).

4. **Expression D**: \((974x^{12}y)^0\)
\[
= 1
\]
This expression is equal to 1.

Since all three of the first expressions are NOT equal to 1 depending on the value of \(x\) (though exactly by scope all three include the value of zero in multiplicative terms which yield to non-uniqueness), whereas the last expression simplifies directly to 1, the answer potentially could be all three depending on the situational values.

However, as originally stated, we just needed to choose the expression that is definitively NOT equivalent to 1 under all conditions.

Thus, to answer your question definitively,

**The expression that is NOT equivalent to (3x to the fourth power) to the zero power is:**
**All three are not equivalent: 1 becoming 0, 1 becoming \(\frac{3}{2}\), and dependency on \(x\) does not produce 1 consistently. Thus, all three are technically incorrect except D**.

Definitively the show could land on
\(3x^2(1/2) x^{-2}\) = \(\frac{3}{2}\)
as explicitly wrong yield towards direct 1 output compared to (3x to the 4th power)^0 = 1 depending; nevertheless, \(x^4 \cdot 0\) converges to 0 conceptually disqualifies equivalently all.

Hope this helps clarify why all outputs allow conditional pitches against that initial zero output by diverging conclusions right after zero allowances for coefficients!