It looks like there's a typo in your equation, specifically at \( 10^{4=} \). I assume you meant \( 16 \cdot 10^4 \) in the denominator. Let's correct it and simplify the following expression:

\[
\frac{8 \cdot 10^7}{16 \cdot 10^4}
\]

### Step 1: Simplify the coefficients
\[
\frac{8}{16} = \frac{1}{2}
\]

### Step 2: Apply the exponent rules for powers of 10
\[
\frac{10^7}{10^4} = 10^{7-4} = 10^3
\]

### Step 3: Combine the simplified components
\[
\frac{1}{2} \cdot 10^3 = 0.5 \cdot 10^3 = 5 \cdot 10^2
\]

### Final Answer:
\[
\frac{8 \cdot 10^7}{16 \cdot 10^4} = 5 \cdot 10^2 = 500
\]

Would you like more details on exponent rules or any specific step?

### Related Questions:
1. What are the rules for simplifying powers of 10 in division?
2. How do you handle coefficients in scientific notation?
3. What is the general approach for simplifying large numbers using powers of 10?
4. How can you rewrite a decimal like \( 0.5 \times 10^3 \) in standard form?
5. What are common mistakes when working with scientific notation?

### Tip:
When dividing terms in scientific notation, handle the coefficients and powers of 10 separately for easier simplification.

Learn how to simplify the expression \( \frac{8 \cdot 10^7}{16 \cdot 10^4} \) using scientific notation and exponent rules. This detailed step-by-step solution covers how to handle coefficients and powers of 10 in division, suitable for students in Grades 8-10.

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