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Multiply. $\newline$ $(2 \times 10^3)(4 \times 10^2)$ $\newline$ Choices: $\newline$ (A) $8 \times 10^4$ $\newline$ (B) $8 \times 10^7$ $\newline$ (C) $8 \times 10^{11}$ $\newline$ (D) $8 \times 10^5$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(2 \times 10^3)(4 \times 10^2)

\newline

Choices:

\newline

(A)

8 \times 10^4

\newline

(B)

8 \times 10^7

\newline

(C)

8 \times 10^{11}

\newline

(D)

8 \times 10^5

Group Coefficients and Power Terms: We have the expression $2 \times 10^3$ ( $4$ \times $10$ ^ $2$ \). First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $2$ and $4$ $\newline$ Power terms: $10^3$ 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 $10^3 \times 10^2$ 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 Final Answer in Scientific Notation: We have found the coefficient to be $8$ and the power term to be $10^5$ . Now, we write the final answer in scientific notation by combining these two results. $\newline$ Scientific notation: $8 \times 10^5$

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