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Multiply. $\newline$ $(3 \times 10^4)(2 \times 10^1)$ $\newline$ Choices: $\newline$ (A) $6 \times 10^4$ $\newline$ (B) $5 \times 10^4$ $\newline$ (C) $5 \times 10^5$ $\newline$ (D) $6 \times 10^5$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(3 \times 10^4)(2 \times 10^1)

\newline

Choices:

\newline

(A)

6 \times 10^4

\newline

(B)

5 \times 10^4

\newline

(C)

5 \times 10^5

\newline

(D)

6 \times 10^5

Group Terms: We have the expression $(3 \times 10^4)(2 \times 10^1)$ . First, we need to group the coefficients and the power terms together. $\newline$ Coefficients: $3$ and $2$ $\newline$ Power terms: $10^4$ and $10^1$
Multiply Coefficients: Multiply the coefficients together. What is $3 \times 2$ ? $\newline$ $3 \times 2 = 6$
Combine Power Terms: Combine the power terms $10^4$ and $10^1$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^4 \times 10^1$ $\newline$ = $10^{4 + 1}$ $\newline$ = $10^5$
Write in Scientific Notation: We have found the coefficient to be $6$ and the power term to be $10^5$ . Now, we write the final answer in scientific notation by combining the coefficient and the power term. $\newline$ Scientific notation: $6 \times 10^5$

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