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Simplify. Your answer should be in proper scientific notation:

(2.5 ×10^(4))(4×10^(3))

Simplify. Your answer should be in proper scientific notation: $\newline$ $\left(2.5 \times 10^{4}\right)\left(4 \times 10^{3}\right)$

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Product property of logarithms

Full solution

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

\newline

\left(2.5 \times 10^{4}\right)\left(4 \times 10^{3}\right)

Multiply Coefficients: Multiply the coefficients ( $2.5$ and $4$ ). $\newline$ Reasoning: In scientific notation, when multiplying two numbers, you multiply their coefficients separately from their powers of ten. $\newline$ Calculation: $2.5 \times 4 = 10$ $\newline$ Math error check:
Add Exponents: Add the exponents ( $4$ and $3$ ) of the powers of ten. $\newline$ Reasoning: When multiplying powers of ten, you add the exponents according to the law of exponents for multiplication. $\newline$ Calculation: $10^4 \times 10^3 = 10^{4+3} = 10^7$ $\newline$ Math error check:
Combine Results: Combine the results from Step $1$ and Step $2$ to form the product in scientific notation. $\newline$ Reasoning: The product of two numbers in scientific notation is the product of their coefficients multiplied by $10$ raised to the sum of their exponents. $\newline$ Calculation: $(2.5 \times 10^4) \times (4 \times 10^3) = 10 \times 10^7$ $\newline$ Math error check:
Ensure Proper Coefficient: Ensure the coefficient is between $1$ and $10$ for proper scientific notation. $\newline$ Reasoning: Proper scientific notation requires the coefficient to be a number between $1$ and $10$ . $\newline$ Calculation: Since the coefficient is $10$ , which is not between $1$ and $10$ , we need to adjust it. We can write $10$ as $1.0 \times 10^1$ . $\newline$ Math error check:
Adjust Final Result: Adjust the final result to reflect the change in the coefficient. $\newline$ Reasoning: After changing the coefficient to fit the proper scientific notation, we need to combine it with the existing power of ten. $\newline$ Calculation: $1.0 \times 10^1 \times 10^7 = 1.0 \times 10^{1+7} = 1.0 \times 10^8$ $\newline$ Math error check:

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