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

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

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

\newline

______

Group Coefficients and Powers: We have the expression $(2 \times 10^3)(2 \times 10^2)$ . First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $2$ and $2$ $\newline$ Power terms: $10^3$ and $10^2$
Multiply Coefficients: Multiply the coefficients together. What is $2 \times 2$ ? $\newline$ $2 \times 2 = 4$
Combine Power Terms: Combine the power terms $10^3 \times 10^2$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^3 \times 10^2 = 10^{3 + 2} = 10^5$
Write in Scientific Notation: We have found the coefficient to be $4$ and the power term to be $10^5$ . Now, we write the final answer in scientific notation by substituting $4$ for the coefficient $a$ and $5$ for the exponent $b$ in the form $a \times 10^b$ . $\newline$ Scientific notation: $4 \times 10^5$

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