What is the standard arithmetic rule for floating-point multiplication: $(M_1 \times 2^{E_1}) \times (M_2 \times 2^{E_2})$?

According to the laws of exponents and floating-point arithmetic (IEEE 754), when multiplying two floating-point numbers: $(M_1 \cdot 2^{E_1}) \cdot (M_2 \cdot 2^{E_2}) = (M_1 \cdot M_2) \cdot 2^{E_1 + E_2}$. Thus, you multiply the mantissas (significands) and add the exponents (accounting for exponent bias).

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