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------------------------------------------------ Write \(8.12 \times 10^{-6} \times 2.00 \times 10^{-5}\) in scientific notation.

a) \(1.62 \times 10^{-10}\)

b) \(1.62 \times 10^{-10}\)

c) \(1.62 \times 10^{-10}\)

d) \(1.62 \times 10^{-10}\)

To multiply 8.12x10⁻⁶ by 2.00x10⁻⁵ in scientific notation, multiply the base numbers and add the exponents to get 1.62x10⁻¹⁰ as the final answer in proper scientific notation.

Explanation:

The student's question involves multiplying two numbers expressed in scientific notation and providing the correct result, also in scientific notation. To multiply two numbers in scientific notation, you multiply their base numbers and add the exponents. Using this method, the answer is calculated as follows:

Multiply the base numbers: 8.12 × 2.00 = 16.24.
Add the exponents: -6 + -5 = -11.
The product in scientific notation is 1.624 × 10⁻¹ⁱ. However, we need to adjust the base number to be between 1 and 10 for proper scientific notation. So, we shift one decimal place to get 1.624 to 1.62 and add 1 to the exponent to compensate for the shift: 1.62 × 10⁻¹¹².

In conclusion, the answer in proper scientific notation is 1.62 × 10⁻¹⁰.