Let's work through questions 27 through 30 step by step.

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27. Simplify $(2 \times 10^6)(1.9 \times 10^1)$:

Multiply the coefficients and add the exponents:

$(2 \times 1.9) \times 10^{6+1} = 3.8 \times 10^7$

Answer: $3.8 \times 10^7$

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28. Simplify $(2 \times 10^2)(7.4 \times 10^6)$:

Multiply the coefficients and add the exponents:

$(2 \times 7.4) \times 10^{2+6} = 14.8 \times 10^8$

Now rewrite $14.8$ as $1.48 \times 10^1$, and adjust the exponent:

$1.48 \times 10^9$

Answer: $1.48 \times 10^9$

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29. Simplify $\frac{4.6 \times 10^4}{1.3 \times 10^{-2}}$:

Divide the coefficients and subtract the exponents:

$\frac{4.6}{1.3} \times 10^{4 - (-2)} = 3.54 \times 10^{4+2} = 3.54 \times 10^6$

Answer: $3.54 \times 10^6$

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30. Simplify $\frac{3.52 \times 10^2}{6.56 \times 10^{-4}}$:

Divide the coefficients and subtract the exponents:

$\frac{3.52}{6.56} \times 10^{2 - (-4)} = 0.536 \times 10^{2+4} = 0.536 \times 10^6$

Now rewrite $0.536$ as $5.36 \times 10^{-1}$, and adjust the exponent:

$5.36 \times 10^5$

Answer: $5.36 \times 10^5$

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Do you have any questions, or would you like further explanations?

Here are 5 related questions to expand your understanding:

1. How do you rewrite $12.3 \times 10^5$ in proper scientific notation?
2. What happens if the exponents in a multiplication problem are negative?
3. How do you simplify $(3.1 \times 10^4)(4.0 \times 10^3)$?
4. How can you divide numbers in scientific notation without a calculator?
5. Why is it important to adjust the coefficient to be between 1 and 10 in scientific notation?

Tip: Always check the coefficient to ensure it is between $1$ and $10$ when writing final answers in scientific notation!