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Multiply. Write your answer in scientific notation. $\newline$ $(2 \times 10^1)(2 \times 10^5)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

(2 \times 10^1)(2 \times 10^5)

\newline

______

Identify Numbers: Identify the numbers to be multiplied. $\newline$ We have: $2 \times 10^1$ ( $2$ \times $10$ ^ $5$ )(\newline\)Group the coefficients and power terms together. $\newline$ Coefficients: $2$ and $2$ $\newline$ Power terms: $10^1$ and $10^5$
Group Coefficients and Power: Multiply the coefficients. $\newline$ Calculate $2 \times 2$ . $\newline$ $2 \times 2 = 4$
Multiply Coefficients: Combine the power terms. $\newline$ Write $10^1 \times 10^5$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^1 \times 10^5$ $\newline$ $= 10^{(1 + 5)}$ $\newline$ $= 10^6$
Combine Power Terms: Combine the results from Step $2$ and Step $3$ to write the final answer in scientific notation. $\newline$ Coefficient = $4$ $\newline$ Power term = $10^6$ $\newline$ Scientific notation: $4 \times 10^6$

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