To simplify the expression \((12a^3)^0(14b)^2\), we can break it down step by step.
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Evaluate \((12a^3)^0\): Any non-zero expression raised to the power of 0 equals 1. Thus, \((12a^3)^0 = 1\).
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Evaluate \((14b)^2\): This involves squaring both the coefficient and the variable: \((14b)^2 = (14^2)(b^2) = 196b^2\).
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Combine the results: Finally, since \((12a^3)^0 = 1\), the entire expression simplifies to: \[ 1 \cdot 196b^2 = 196b^2. \]
Now, let's evaluate the provided responses and see which can be simplified to \(196b^2\):
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Response 1: \((1/2)^0 \times a^{3 \cdot 0} \times (14)^2 \times b^2\)
- This simplifies to \(1 \cdot 1 \cdot 196 \cdot b^2 = 196b^2\).
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Response 2: \(1 \times 1 \times 1/4 \times 1/4 \times b \times b\)
- This simplifies to \(1 \times 1 \times \frac{1}{16} \times b^2 = \frac{1}{16}b^2\), which is not \(196b^2\).
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Response 3: \(0\)
- This is not equivalent to \(196b^2\).
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Response 4: \((1/2)^0 \times a^{3 + 0} \times (1/4)^2 \times b^2\)
- This simplifies to \(1 \cdot a^3 \cdot \frac{1}{16} \cdot b^2 = \frac{1}{16}a^3b^2\), which is not equal to \(196b^2\).
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Response 5: \(1/16b^2\)
- This is not equal to \(196b^2\).
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Response 6: \(0 \times 0 \times \frac{1}{4} \times \frac{1}{4} \times b \times b\)
- This is equal to \(0\), not \(196b^2\).
Conclusion
The only equivalent expression to the original expression \((12a^3)^0(14b)^2\) is:
- Response 1: \((1/2)^0 \times a^{3 \cdot 0} \times (14)^2 \times b^2\)
Thus, the answer is:
Equivalent expression: \((1/2)^0 \times a^{3 \cdot 0} \times (14)^2 \times b^2\)
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