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

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

\newline

______

Group Terms: We have the expression $2 \times 10^2$ $(4 \times 10^2)$ . First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $2$ and $4$ $\newline$ Power terms: $10^2$ and $10^2$
Multiply Coefficients: Multiply the coefficients together. What is $2 \times 4$ ? $\newline$ $2 \times 4 = 8$
Combine Power Terms: Combine the power terms $10^2 \times 10^2$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^2 \times 10^2$ $\newline$ $= 10^{(2 + 2)}$ $\newline$ $= 10^4$
Final Scientific Notation: We have found: $\newline$ Coefficient = $8$ $\newline$ Power term = $10^4$ $\newline$ Now, we write the final answer in scientific notation by substituting $8$ for the coefficient and $4$ for the exponent. $\newline$ Scientific notation: $8 \times 10^4$

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