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Multiply. Write your answer in scientific notation. $\newline$ $(3 \times 10^5)(3 \times 10^2)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

(3 \times 10^5)(3 \times 10^2)

\newline

______

Identify Components: Identify the components of the multiplication problem. $\newline$ We have: 3 \times 10^5)(3 \times 10^2)\. We need to group the coefficients \$3 and $3$ and the power terms $10^5$ and $10^2$ together.
Multiply Coefficients: Multiply the coefficients. $\newline$ What is $3 \times 3$ ? Multiply the coefficients together. $\newline$ $3 \times 3 = 9$
Combine Power Terms: Combine the power terms into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $10^5 \times 10^2$ can be written as $10^{(5 + 2)}$ . Calculating the exponent sum: $5 + 2 = 7$ . So, $10^5 \times 10^2 = 10^7$ .
Write Final Answer: Write the final answer in scientific notation. $\newline$ We found: $\newline$ Coefficient = $9$ $\newline$ Power term = $10^7$ $\newline$ Combine these to write the final answer in scientific notation: $9 \times 10^7$ .

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