\frac{4n^{-4}}{n^3} simplify with only positive exponents

To simplify the expression \(\frac{4n^{-4}}{n^3}\) with only positive exponents, follow these steps:

1. **Combine the exponents of \(n\):**
   \[
   \frac{4n^{-4}}{n^3} = 4 \cdot n^{-4 - 3}
   \]
   The exponents are added because you are dividing powers of the same base \(n\).

2. **Simplify the exponent:**
   \[
   4 \cdot n^{-7}
   \]
   This results from adding \(-4\) and \(-3\).

3. **Convert the negative exponent to a positive exponent:**
   \[
   4 \cdot \frac{1}{n^7} = \frac{4}{n^7}
   \]

So, the simplified expression with only positive exponents is:
\[
\frac{4}{n^7}
\]

Would you like any further details or have any questions?

Here are 8 related questions to expand on this:

1. How do you handle division when both the numerator and denominator have negative exponents?
2. Can you explain the rules of exponents when multiplying or dividing powers of the same base?
3. What happens if both exponents were positive in the initial expression?
4. How would the result change if the numerator had a different base?
5. How do you simplify expressions involving both positive and negative exponents?
6. What is the rule for converting a negative exponent into a positive one?
7. Can you provide a similar example with a more complex expression?
8. What is the general form of simplifying expressions with exponents?

**Tip:** Always check your final expression to ensure all exponents are positive when the problem asks for it.

Learn how to simplify the expression \(\frac{4n^{-4}}{n^3}\) with only positive exponents. Follow a detailed step-by-step solution to understand the process of combining and converting exponents. Suitable for Grades 7-9.

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