Multiply. (2 * 10^2)(4 * 10^2) Choices: (A)3 * 10^4 (B)5 * 10^4 (C)9 * 10^4 (D)8 * 10^4

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

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Multiply. $\newline$ $(2 \times 10^2)(4 \times 10^2)$ $\newline$ Choices: $\newline$ (A) $3 \times 10^4$ $\newline$ (B) $5 \times 10^4$ $\newline$ (C) $9 \times 10^4$ $\newline$ (D) $8 \times 10^4$

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Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

3 \times 10^4

\newline

(B)

5 \times 10^4

\newline

(C)

9 \times 10^4

\newline

(D)

8 \times 10^4

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