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Multiply. Write your answer in scientific notation. $\newline$ $(4 \times 10^1)(2 \times 10^3)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

(4 \times 10^1)(2 \times 10^3)

\newline

______

Identify Numbers: Identify the numbers to be multiplied. $\newline$ We have: $4 \times 10^1$ ( $2$ \times $10$ ^ $3$ \) $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $4$ and $2$ $\newline$ Power terms: $10^1$ and $10^3$
Group Coefficients and Power: Multiply the coefficients. $\newline$ Calculate $4 \times 2$ . $\newline$ $4 \times 2 = 8$
Multiply Coefficients: Multiply the power terms. $\newline$ Write $10^1 \times 10^3$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^1 \times 10^3$ $\newline$ $= 10^{1 + 3}$ $\newline$ $= 10^4$
Multiply Power Terms: Combine the results from Step $2$ and Step $3$ . $\newline$ 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: $8 \times 10^4$

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