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Multiply. Write your answer in scientific notation. $\newline$ $(5 \times 10^1)(1 \times 10^5)$ $\newline$ ______

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Multiply numbers written in scientific notation

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Q. Multiply. Write your answer in scientific notation.

\newline

(5 \times 10^1)(1 \times 10^5)

\newline

______

Group Coefficients and Power Terms: We have: $\newline$ $(5 \times 10^1)(1 \times 10^5)$ $\newline$ Group the coefficients and power terms together. $\newline$ Coefficients: $5$ and $1$ $\newline$ Power terms: $10^1$ and $10^5$
Multiply Coefficients: What is $5 \times 1$ ? Multiply the coefficients. $\newline$ $5 \times 1 = 5$
Combine Power Terms: Write $10^1 \times 10^5$ as a single power of $10$ . When multiplying powers with the same base, we add the exponents. $\newline$ $10^1 \times 10^5$ $\newline$ $= 10^{(1 + 5)}$ $\newline$ $= 10^6$
Write Final Answer: We found: $\newline$ Coefficient = $5$ $\newline$ Power term = $10^6$ $\newline$ Write the final answer in scientific notation. Substitute $5$ for $a$ and $6$ for $b$ in $a \times 10^b$ . $\newline$ Scientific notation: $5 \times 10^6$

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