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Multiply. $\newline$ $(1 \times 10^1)(6 \times 10^3)$ $\newline$ Choices: $\newline$ (A) $6 \times 10^4$ $\newline$ (B) $6 \times 10^7$ $\newline$ (C) $6 \times 10^9$ $\newline$ (D) $6 \times 10^0$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(1 \times 10^1)(6 \times 10^3)

\newline

Choices:

\newline

(A)

6 \times 10^4

\newline

(B)

6 \times 10^7

\newline

(C)

6 \times 10^9

\newline

(D)

6 \times 10^0

Group Coefficients and Powers: We have the expression $1 \times 10^1$ ( $6$ \times $10$ ^ $3$ \). First, we group the coefficients and power terms together. $\newline$ Coefficients: $1$ and $6$ $\newline$ Power terms: $10^1$ and $10^3$
Multiply Coefficients: Multiply the coefficients together. $1 \times 6 = 6$
Multiply Power Terms: Multiply the power terms together. When multiplying powers with the same base, we add the exponents. $\newline$ $10^1 \times 10^3 = 10^{(1 + 3)} = 10^4$
Combine Results: Combine the results from Step $2$ and Step $3$ to write the final answer in scientific notation. $\newline$ Coefficient = $6$ $\newline$ Power term = $10^4$ $\newline$ Scientific notation: $6 \times 10^4$

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