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Multiply. $\newline$ $(3 \times 10^4)(3 \times 10^3)$ $\newline$ Choices: $\newline$ (A) $6 \times 10^7$ $\newline$ (B) $9 \times 10^{12}$ $\newline$ (C) $6 \times 10^{12}$ $\newline$ (D) $9 \times 10^7$

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Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

6 \times 10^7

\newline

(B)

9 \times 10^{12}

\newline

(C)

6 \times 10^{12}

\newline

(D)

9 \times 10^7

Group Terms: We have: $\newline$ $(3 \times 10^4)(3 \times 10^3)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $3$ and $3$ $\newline$ Power terms: $10^4$ and $10^3$
Multiply Coefficients: What is $3 \times 3$ ? Multiply the coefficients. $\newline$ $3 \times 3 = 9$
Combine Power Terms: Write $10^4 \times 10^3$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^4 \times 10^3$ $\newline$ $= 10^{4 + 3}$ $\newline$ $= 10^7$
Final Scientific Notation: We found: $\newline$ Coefficient = $9$ $\newline$ Power term = $10^7$ $\newline$ Write the final answer in scientific notation. Substitute $9$ for $a$ and $7$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $9 \times 10^7$

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