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Simplify. Your answer should be in proper scientific notation

25(8×10^(3))

Simplify. Your answer should be in proper scientific notation $\newline$ $25\left(8 \times 10^{3}\right)$

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Evaluate rational exponents

Full solution

Q. Simplify. Your answer should be in proper scientific notation

\newline

25\left(8 \times 10^{3}\right)

Identify Numbers and Operation: Identify the numbers to be multiplied and the operation to be performed. $\newline$ We have $25$ and $8\times10^{3}$ to be multiplied together. $\newline$ Calculation: None needed at this step.
Multiply Coefficients: Multiply the coefficients (numerical parts) together. $25$ multiplied by $8$ equals $200$ . Calculation: $25 \times 8 = 200$
Combine with Power of $10$ : Combine the result from the previous step with the power of $10$ . $\newline$ Since $8\times10^{3}$ has a power of $10$ , we simply attach $10^{3}$ to the result of the multiplication of the coefficients. $\newline$ Calculation: $200 \times 10^{3}$
Express in Scientific Notation: Express the result in proper scientific notation. $\newline$ Proper scientific notation requires a number between $1$ and $10$ multiplied by a power of $10$ . The number $200$ is not between $1$ and $10$ , so we need to adjust it. $\newline$ Calculation: $200$ can be written as $2 \times 10^{2}$ , so the expression becomes $2 \times 10^{2} \times 10^{3}$ .
Combine Powers of $10$ : Combine the powers of $10$ using the rule of exponents (adding the exponents when multiplying with the same base). $\newline$ Calculation: $2 \times 10^{2+3} = 2 \times 10^{5}$
Final Answer: Write the final answer in proper scientific notation. $\newline$ Calculation: The final answer is $2 \times 10^{5}$ .

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