Final answer:
When multiplying (6.30x10⁴) by (5.424x10³), which involves multiplying the significant numbers and adding the exponents, the closest answer is option (b) 3414.72x10⁸ in proper scientific notation: 3.41472x10⁸.
Step-by-step explanation:
The multiplication of two numbers in scientific notation involves multiplying the significant figures and adding the exponents of the ten. In the case of (6.30\u00d710⁴) \u00d7 (5.424\u00d710³), the significant figures are 6.30 and 5.424, which multiply to yield approximately 34.1712. The exponents of ten are 4 and 3, which add up to 7. We express 34.1712 as 3.41712 \u00d7 10, shifting the decimal point one place to ensure the number is between 1 and 10, so the exponent increases by 1, yielding a combined exponent of 8.
The correct scientific notation for the product is therefore 3.41712\u00d710⁸. However, due to significant figures, the result as given in the options would be truncated to 3.4172\u00d710⁸, which none of the options exactly match. But based on the closest correct mathematical representation, option (b) 3414.72\u00d710⁸ is the closest to the calculated result when written in proper scientific notation, which would be 3.41472\u00d710⁸.