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

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

4 \times 10^{10}

\newline

(B)

4 \times 10^7

\newline

(C)

7 \times 10^7

\newline

(D)

7 \times 10^{10}

Multiply Coefficients: We have the expression $(2 \times 10^5)(2 \times 10^2)$ . First, we need to multiply the coefficients $2$ and $2$ together. $\newline$ Calculation: $2 \times 2 = 4$
Multiply Power Terms: Next, we need to multiply the power terms ( $10^5$ and $10^2$ ) together. When multiplying powers with the same base, we add the exponents. $\newline$ Calculation: $10^5 \times 10^2 = 10^{5 + 2} = 10^7$
Combine Results: Combine the results from Step $1$ and Step $2$ to write the final answer in scientific notation. $\newline$ Calculation: $4 \times 10^7$

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