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Multiply. Write your answer in scientific notation. $\newline$ $(4 \times 10^2)(2 \times 10^5)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

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

\newline

______

Identify Components: Identify the components of the multiplication problem. $\newline$ We have: $\newline$ $(4 \times 10^2)(2 \times 10^5)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $4$ and $2$ $\newline$ Power terms: $10^2$ and $10^5$
Multiply Coefficients: Multiply the coefficients. $\newline$ Calculate $4 \times 2$ . $\newline$ $4 \times 2 = 8$
Combine Power Terms: Combine the power terms into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $10^2 \times 10^5 = 10^{2 + 5} = 10^7$
Write Final Answer: Combine the results from Step $2$ and Step $3$ to write the final answer in scientific notation. $\newline$ Coefficient = $8$ $\newline$ Power term = $10^7$ $\newline$ Scientific notation: $8 \times 10^7$

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