Multiply. (4 * 10^1)(2 * 10^5) Choices: (A)4 * 10^6 (B)3 * 10^6 (C)8 * 10^6 (D)7 * 10^6

Group Coefficients and Power Terms: We have: (4 × 10^1)(2 × 10^5) Group the coefficients and power terms together. Coefficients: 4 and 2 Power terms: 10^1 and 10^5Multiply Coefficients: What is 4 × 2? Multiply the coefficients. 4 × 2 = 8Combine Power Terms: Write 10^1 × 10^5 as a single power of 10. When multiplying powers with the same base, we add the exponents. 10^1 × 10^5 = 10^(1 + 5) = 10^6Write Final Answer: We found: Coefficient = 8 Power term = 10^6 Write the final answer in scientific notation. Substitute 8 for a and 6 for b in a × 10^b. Scientific notation: 8 × 10^6

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Multiply. $\newline$ $(4 \times 10^1)(2 \times 10^5)$ $\newline$ Choices: $\newline$ (A) $4 \times 10^6$ $\newline$ (B) $3 \times 10^6$ $\newline$ (C) $8 \times 10^6$ $\newline$ (D) $7 \times 10^6$

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Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(4 \times 10^1)(2 \times 10^5)

\newline

Choices:

\newline

(A)

4 \times 10^6

\newline

(B)

3 \times 10^6

\newline

(C)

8 \times 10^6

\newline

(D)

7 \times 10^6

Group Coefficients and Power Terms: We have: $\newline$ $(4 \times 10^1)(2 \times 10^5)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $4$ and $2$ $\newline$ Power terms: $10^1$ and $10^5$
Multiply Coefficients: What is $4 \times 2$ ? Multiply the coefficients. $\newline$ $4 \times 2 = 8$
Combine Power Terms: Write $10^1 \times 10^5$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^1 \times 10^5$ $\newline$ $= 10^{(1 + 5)}$ $\newline$ $= 10^6$
Write Final Answer: We found: $\newline$ Coefficient = $8$ $\newline$ Power term = $10^6$ $\newline$ Write the final answer in scientific notation. Substitute $8$ for $a$ and $6$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $8 \times 10^6$