To solve $(8 \times 10^7) \div (4 \times 10^5)$, follow these steps:

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Step 1: Divide the coefficients

$\frac{8}{4} = 2$

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Step 2: Subtract the powers of 10

Using the rule $\frac{10^a}{10^b} = 10^{a-b}$: $10^{7-5} = 10^2$

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Step 3: Combine the results

$2 \times 10^2$

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Final Answer:

$\boxed{2 \times 10^2}$

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Let me know if you want detailed reasoning or have any further questions! Here are 5 related questions to explore:

1. What are the general rules for dividing numbers in standard form?
2. How do you multiply numbers in standard form?
3. Can you convert $2 \times 10^2$ into its decimal form?
4. How would you handle $(5 \times 10^3) \div (2.5 \times 10^1)$?
5. How do standard form rules apply to negative powers of 10?

Tip: Always ensure coefficients in standard form are between 1 and 10 to maintain correct notation!