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The expression you provided is:

\[
\frac{8a}{4a^7}
\]

We can simplify this by dividing both the numerator and denominator.

### Step 1: Simplify the coefficients
\[
\frac{8}{4} = 2
\]

### Step 2: Simplify the powers of \(a\)
Using the rule of exponents \(\frac{a^m}{a^n} = a^{m-n}\), we have:

\[
\frac{a}{a^7} = a^{1-7} = a^{-6}
\]

### Step 3: Combine the results
\[
\frac{8a}{4a^7} = 2a^{-6}
\]

The final simplified expression is:

\[
2a^{-6}
\]

Alternatively, if you want the expression without negative exponents, you can write it as:

\[
\frac{2}{a^6}
\]

Would you like any further explanation or details?

Here are 5 related questions to explore further:
1. How do negative exponents relate to division?
2. Can we simplify more complex rational expressions using these rules?
3. How do the rules of exponents apply to other variables, not just \(a\)?
4. What happens if the exponent in the denominator is larger or smaller?
5. How do fractional exponents impact the simplification process?

**Tip:** Remember, when dividing exponents with the same base, subtract the exponents!

Learn how to simplify the expression 8a / 4a^7 by using the rules of exponents. This solution walks through simplifying coefficients and managing exponents step by step, suitable for students in Grades 7-9.

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