Multiply. (4 * 10^3)(2 * 10^4) Choices: (A)6 * 10^12 (B)8 * 10^12 (C)6 * 10^7 (D)8 * 10^7

Group Coefficients and Power Terms: We have: (4 × 10^3)(2 × 10^4) Group the coefficients and power terms together. Coefficients: 4 and 2 Power terms: 10^3 and 10^4Multiply Coefficients: What is 4 × 2? Multiply the coefficients. 4 × 2 = 8Combine Power Terms: Write 10^3 × 10^4 as a single power of 10. When multiplying powers with the same base, we add the exponents. 10^3 × 10^4 = 10^(3 + 4) = 10^7Final Scientific Notation: We found: Coefficient = 8 Power term = 10^7 Write the final answer in scientific notation. Substitute 8 for a and 7 for b in a × 10^b. Scientific notation: 8 × 10^7

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Multiply. $\newline$ $(4 \times 10^3)(2 \times 10^4)$ $\newline$ Choices: $\newline$ (A) $6 \times 10^{12}$ $\newline$ (B) $8 \times 10^{12}$ $\newline$ (C) $6 \times 10^7$ $\newline$ (D) $8 \times 10^7$

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Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

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Choices:

\newline

(A)

6 \times 10^{12}

\newline

(B)

8 \times 10^{12}

\newline

(C)

6 \times 10^7

\newline

(D)

8 \times 10^7

Group Coefficients and Power Terms: We have: $\newline$ $(4 \times 10^3)(2 \times 10^4)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $4$ and $2$ $\newline$ Power terms: $10^3$ and $10^4$
Multiply Coefficients: What is $4 \times 2$ ? Multiply the coefficients. $\newline$ $4 \times 2 = 8$
Combine Power Terms: Write $10^3 \times 10^4$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^3 \times 10^4$ $\newline$ $= 10^{3 + 4}$ $\newline$ $= 10^7$
Final Scientific Notation: We found: $\newline$ Coefficient = $8$ $\newline$ Power term = $10^7$ $\newline$ Write the final answer in scientific notation. Substitute $8$ for $a$ and $7$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $8 \times 10^7$