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Perform the multiplication and express the result in scientific notation: (6.4×10⁵)×(36,000).

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Final answer:

To multiply (6.4×10⁵) by (36,000), first convert 36,000 to scientific notation (3.6×10⁴), multiply the base numbers (6.4×3.6), and add the exponents (5+4) to obtain the final result: 2.304×10⁹.

Step-by-step explanation:

Understanding Scientific Notation Multiplication

When multiplying two numbers in scientific notation, such as (6.4×10⁵) and (36,000), you convert all numbers into scientific notation and then multiply the base numbers and add the exponents. First, represent 36,000 in scientific notation, which is 3.6×10⁴. Now, multiply the numbers:

(6.4×10⁵) × (3.6×10⁴) = (6.4 × 3.6) × 10⁵ × 10⁴

Multiplying the base numbers: 6.4 × 3.6 gives 23.04. Adding the exponents: 5 + 4 gives 9. Therefore, the final result in scientific notation is 2.304×10⁹

In summary, we have converted the original expression into scientific notation, multiplied the base numbers, and added the exponents to reach the final answer.

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