To simplify the expression \(2b^3 \times 1b^4\), we first rewrite it in a clearer format:
\[ 2b^3 \times 1b^4 = 2 \times 1 \times b^3 \times b^4 \]
Now, simplify it step by step:
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Multiply the constants: \[ 2 \times 1 = 2 \]
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Combine the powers of \(b\) using the property \(b^m \times b^n = b^{m+n}\): \[ b^3 \times b^4 = b^{3+4} = b^7 \]
Now putting it all together, we have: \[ 2b^3 \times 1b^4 = 2b^7 \]
Thus, the simplified expression is \(2b^7\).
From your options, it seems none of them directly represent \(2b^7\), but if you're looking for expressions involving \(b\) raised to the 7th power, then \(3B^7\) or \(B^{12}\) do not apply in this context.
The correct answer to the multiplication \(2b^3 \times 1b^4\) is \(2b^7\).