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

Group Coefficients and Power Terms: We have the expression (4 * 10^2)(2 * 10^5). First, we need to group the coefficients (4 and 2) and the power terms (10^2 and 10^5) together. Coefficients: 4 and 2 Power terms: 10^2 and 10^5Multiply Coefficients: Multiply the coefficients together. What is 4 × 2? 4 × 2 = 8Combine Power Terms: Combine the power terms 10^2 × 10^5 into a single power of 10. When multiplying powers with the same base, we add the exponents. 10^2 × 10^5 = 10^(2 + 5) = 10^7Write in Scientific Notation: We have found the coefficient to be 8 and the power term to be 10^7. Now, we write the final answer in scientific notation by substituting 8 for the coefficient and 7 for the exponent. Scientific notation: 8 × 10^7

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 1

Multiply numbers written in scientific notation

Full solution

Q. Multiply.

\newline

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

\newline

Choices:

\newline

(A)

8 \times 10^{10}

\newline

(B)

6 \times 10^{10}

\newline

(C)

6 \times 10^7

\newline

(D)

8 \times 10^7

Group Coefficients and Power Terms: We have the expression $4 \times 10^2$ $(2 \times 10^5)$ . First, we need to group the coefficients $4$ and $2$ and the power terms $10^2$ and $10^5$ together. $\newline$ Coefficients: $4$ and $2$ $\newline$ Power terms: $10^2$ and $10^5$
Multiply Coefficients: Multiply the coefficients together. What is $4 \times 2$ ? $\newline$ $4 \times 2 = 8$
Combine Power Terms: Combine the power terms $10^2 \times 10^5$ into a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^2 \times 10^5$ $\newline$ $= 10^{(2 + 5)}$ $\newline$ $= 10^7$
Write in Scientific Notation: We have found the coefficient to be $8$ and the power term to be $10^7$ . Now, we write the final answer in scientific notation by substituting $8$ for the coefficient and $7$ for the exponent. $\newline$ Scientific notation: $8 \times 10^7$