To express \( \frac{4^{111}}{4^{108}} \) as a fraction, we follow the same steps as before but maintain the fraction form until the end:

### Step-by-Step Solution:

1. **Apply the Quotient Rule for Exponents**:
   \[
   \frac{4^{111}}{4^{108}} = 4^{111 - 108}
   \]

2. **Simplify the Exponent**:
   \[
   111 - 108 = 3
   \]
   Thus, \(4^{111 - 108} = 4^3\).

3. **Compute \(4^3\)**:
   \[
   4^3 = 4 \times 4 \times 4 = 64
   \]

4. **Express as a Fraction**:
   Since \(4^3 = 64\), the fraction \(\frac{4^{111}}{4^{108}}\) simplifies to \(64\), which can also be written as:
   \[
   \frac{64}{1}
   \]

### Final Answer as a Fraction:
\[
\frac{4^{111}}{4^{108}} = \frac{64}{1}
\]

So, the fraction form of the result is \(\frac{64}{1}\), which simplifies to \(64\).

Would you like more details or have any other questions?

Here are five related questions that might help expand your understanding:

1. How do you convert other exponents into fraction form when simplifying?
2. What happens if you have a negative exponent in a fraction, such as \( \frac{4^{111}}{4^{112}} \)?
3. How can you express \( \frac{5^{7}}{5^{5}} \) as a fraction?
4. What are the properties of fractions involving powers of 10, like \( \frac{10^{9}}{10^{6}} \)?
5. How does simplifying fractions with exponents differ from adding or subtracting fractions?

**Tip:** When working with exponents and fractions, simplify the exponent first and then compute the power if necessary.

Learn how to simplify the fraction \( \frac{4^{111}}{4^{108}} \) step-by-step with detailed explanations. This problem involves applying the quotient rule for exponents and simplifying powers of 4. Suitable for students in Grades 6-8.

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