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

Group Coefficients and Power Terms: We have: (2 × 10^3)(2 × 10^2) Group the coefficients and power terms together. Coefficients: 2 and 2 Power terms: 10^3 and 10^2Multiply Coefficients: What is 2 × 2? Multiply the coefficients. 2 × 2 = 4Combine Power Terms: Write 10^3 × 10^2 as a single power of 10. When multiplying powers with the same base, we add the exponents. 10^3 × 10^2 = 10^(3 + 2) = 10^5Write Final Answer: We found: Coefficient = 4 Power term = 10^5 Write the final answer in scientific notation. Substitute 4 for a and 5 for b in a × 10^b. Scientific notation: 4 × 10^5

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

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Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

3 \times 10^4

\newline

(B)

4 \times 10^6

\newline

(C)

3 \times 10^5

\newline

(D)

4 \times 10^5

Group Coefficients and Power Terms: We have: $\newline$ $(2 \times 10^3)(2 \times 10^2)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $2$ and $2$ $\newline$ Power terms: $10^3$ and $10^2$
Multiply Coefficients: What is $2 \times 2$ ? Multiply the coefficients. $\newline$ $2 \times 2 = 4$
Combine Power Terms: Write $10^3 \times 10^2$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^3 \times 10^2$ $\newline$ $= 10^{3 + 2}$ $\newline$ $= 10^5$
Write Final Answer: We found: $\newline$ Coefficient = $4$ $\newline$ Power term = $10^5$ $\newline$ Write the final answer in scientific notation. Substitute $4$ for $a$ and $5$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $4 \times 10^5$