Question
Which expression is NOT equivalent to: (3x4)0 (1 point)Responses3x23x⋅x3x23x⋅x3x2⋅(13)x−23 times x squared times 1 third x to the negative 2 power(974x12y)0open paren 974 x to the 12th power y close paren to the 0 powerx4⋅0x3x to the 4th power times 0 x cubed
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Answered by
GPT-4o mini
To determine which expression is NOT equivalent to \((3x^4)^0\), we first need to recognize that any expression raised to the power of 0 is equal to 1, provided that the base is not zero.
Therefore, \((3x^4)^0 = 1\).
Now, let's analyze each of the responses to see if they evaluate to 1:
1. **\(3x^2\)**: This is not equivalent to 1, as it depends on the values of \(x\).
2. **\(3x \cdot x^3\)**: This simplifies to \(3x^4\), which also depends on \(x\) and is not equal to 1.
3. **\(3x^2 \cdot \frac{1}{3}x^{-2}\)**: This can be simplified. The \(3\) and \(\frac{1}{3}\) cancel out, and \(x^2 \cdot x^{-2} = x^{2 - 2} = x^0 = 1\). So, this expression evaluates to 1.
4. **\((974x^{12}y)^0\)**: Any expression to the power of 0 is equal to 1, assuming the base is not zero. So, this evaluates to 1.
5. **\(x^4 \cdot 0\)**: This expression equals 0, which is not equal to 1.
6. **\(x^3\)**: This is not equal to 1; it depends on the value of \(x\).
From this evaluation, the expressions that do not equal 1 are \(3x^2\), \(3x \cdot x^3\), \(x^3\), and \(x^4 \cdot 0\). Since the question asks for just one response that is NOT equivalent to \((3x^4)^0\), multiple options fit this category. However, since \(x^4 \cdot 0\) clearly evaluates to 0, it stands out as the simplest to identify.
Thus, one clear answer is:
**\(x^4 \cdot 0\)** is NOT equivalent to \((3x^4)^0\).
Therefore, \((3x^4)^0 = 1\).
Now, let's analyze each of the responses to see if they evaluate to 1:
1. **\(3x^2\)**: This is not equivalent to 1, as it depends on the values of \(x\).
2. **\(3x \cdot x^3\)**: This simplifies to \(3x^4\), which also depends on \(x\) and is not equal to 1.
3. **\(3x^2 \cdot \frac{1}{3}x^{-2}\)**: This can be simplified. The \(3\) and \(\frac{1}{3}\) cancel out, and \(x^2 \cdot x^{-2} = x^{2 - 2} = x^0 = 1\). So, this expression evaluates to 1.
4. **\((974x^{12}y)^0\)**: Any expression to the power of 0 is equal to 1, assuming the base is not zero. So, this evaluates to 1.
5. **\(x^4 \cdot 0\)**: This expression equals 0, which is not equal to 1.
6. **\(x^3\)**: This is not equal to 1; it depends on the value of \(x\).
From this evaluation, the expressions that do not equal 1 are \(3x^2\), \(3x \cdot x^3\), \(x^3\), and \(x^4 \cdot 0\). Since the question asks for just one response that is NOT equivalent to \((3x^4)^0\), multiple options fit this category. However, since \(x^4 \cdot 0\) clearly evaluates to 0, it stands out as the simplest to identify.
Thus, one clear answer is:
**\(x^4 \cdot 0\)** is NOT equivalent to \((3x^4)^0\).
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