To determine which expression is NOT equivalent to \((3x(4))(0)\), we can simplify this expression first. The expression involves multiplying by zero, which results in zero. Thus:
\[ (3x(4))(0) = 0 \]
Now, let's evaluate each of the given responses to see if any do not simplify to zero.
-
\(3x(2)/3x\cdot x\):
- This simplifies to \((3x^2)/(3x^2) = 1\) (assuming \(x \neq 0\)). This does NOT equal zero.
-
\(3x(2)\cdot(1/3)x(−2)\):
- This simplifies to \(3x^2 \cdot (1/3)x^{-2} = x^2 \cdot x^{-2} = 1\). This does NOT equal zero.
-
\(x(4)\cdot0x(3)\):
- This expression involves \(x^4 \cdot 0\cdot x^3 = 0\). This DOES equal zero.
-
\((974x(12)y)(0)\):
- This expression involves multiplying by zero: \( (974x^{12}y) \cdot 0 = 0\). This DOES equal zero.
From these evaluations, the expressions \(3x(2)/3x\cdot x\) and \(3x(2)\cdot(1/3)x(−2)\) both simplify to \(1\) and are therefore NOT equivalent to zero.
Conclusion: Any of the first two options is NOT equivalent to \((3x(4))(0)\). If only one choice must be picked, you could choose:
\(3x(2)/3x\cdot x\) as a response.