Problem

Multiply the following and express your answer in appropriate scientific notation:
\[
\left(8.1 \times 10^{29}\right) \times\left(9.9 \times 10^{-12}\right)
\]
product $=$
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Answer

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Answer

Final Answer: The product of \(\left(8.1 \times 10^{29}\right) \times\left(9.9 \times 10^{-12}\right)\) is \(\boxed{8.019 \times 10^{18}}\).

Steps

Step 1 :The question is asking to multiply two numbers that are in scientific notation. To multiply numbers in scientific notation, we multiply the coefficients (the numbers before the 'times 10 to the power of' part) and add the exponents. So, we need to multiply 8.1 and 9.9, and then add 29 and -12.

Step 2 :The product of the coefficients is 80.19 and the sum of the exponents is 17.

Step 3 :However, in scientific notation, the coefficient should be a number between 1 and 10. So, we need to adjust the coefficient and exponent to fit this format. We can do this by dividing the coefficient by 10 and adding 1 to the exponent.

Step 4 :The adjusted coefficient is 8.019 and the adjusted exponent is 18.

Step 5 :Final Answer: The product of \(\left(8.1 \times 10^{29}\right) \times\left(9.9 \times 10^{-12}\right)\) is \(\boxed{8.019 \times 10^{18}}\).

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