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

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

\newline

______

Identify Components: Identify the components of the multiplication problem. $\newline$ We have: $\newline$ $(2 \times 10^2)(2 \times 10^4)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $2$ and $2$ $\newline$ Power terms: $10^2$ and $10^4$
Multiply Coefficients: Multiply the coefficients. $\newline$ What is $2 \times 2$ ? Multiply the coefficients. $\newline$ $2 \times 2 = 4$
Combine Power Terms: Combine the power terms into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $10^2 \times 10^4 = 10^{2 + 4} = 10^6$
Write in Scientific Notation: Write the final answer in scientific notation. $\newline$ We found: $\newline$ Coefficient = $4$ $\newline$ Power term = $10^6$ $\newline$ Combine them to write the answer in scientific notation. $\newline$ Scientific notation: $4 \times 10^6$

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