Final answer:
The multiplication of the two numbers in scientific notation, 9.25 x 10⁻⁸ and 6.40 x 10³, results in 5.92 x 10⁴ when adjusted to have a coefficient between 1 and 10.
Step-by-step explanation:
To perform the operation and express the answer in scientific notation, we need to multiply the two given numbers. The question presented is: 9.25 x 10⁻⁸ x 6.40 x 10³. In scientific notation multiplication, we multiply the coefficients and add the exponents.
The coefficient multiplication is 9.25 x 6.40, which equals 59.2. For the exponents, we add -8 and 3, which equals -5. Hence, we can write the intermediate result as 59.2 x 10⁻⁵.
Since scientific notation requires the coefficient to be between 1 and 10, we need to adjust 59.2. We can express 59.2 as 5.92 x 10¹. This adjustment increases the exponent part by 1, so we combine this with the earlier exponent of -5, resulting in 5.92 x 10¹ x 10⁻⁵, which simplifies to 5.92 x 10⁴.
Therefore, the final answer in proper scientific notation is 5.92 x 10⁴.