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

Group Coefficients and Power Terms: We have: (1 × 10^4)(7 × 10^1) Group the coefficients and power terms together. Coefficients: 1 and 7 Power terms: 10^4 and 10^1Multiply Coefficients: What is 1 × 7? Multiply the coefficients. 1 × 7 = 7Combine Power Terms: Write 10^4 × 10^1 as a single power of 10. When multiplying powers with the same base, we add the exponents. 10^4 × 10^1 = 10^(4 + 1) = 10^5Write Final Answer: We found: Coefficient = 7 Power term = 10^5 Write the final answer in scientific notation. Substitute 7 for a and 5 for b in a × 10^b. Scientific notation: 7 × 10^5

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

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Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

(1 \times 10^4)(7 \times 10^1)

\newline

Choices:

\newline

(A)

3 \times 10^5

\newline

(B)

7 \times 10^4

\newline

(C)

3 \times 10^4

\newline

(D)

7 \times 10^5

Group Coefficients and Power Terms: We have: $\newline$ $(1 \times 10^4)(7 \times 10^1)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $1$ and $7$ $\newline$ Power terms: $10^4$ and $10^1$
Multiply Coefficients: What is $1 \times 7$ ? Multiply the coefficients. $\newline$ $1 \times 7 = 7$
Combine Power Terms: Write $10^4 \times 10^1$ as 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 Final Answer: We found: $\newline$ Coefficient = $7$ $\newline$ Power term = $10^5$ $\newline$ Write the final answer in scientific notation. Substitute $7$ for $a$ and $5$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $7 \times 10^5$