Let's solve the expression \(\frac{(-4)^3}{(-4)^5} \div (-4)^4\).

First, let's break down the problem step by step.

1. **Calculate the numerator:**
   \[
   (-4)^3 = (-4) \times (-4) \times (-4) = -64
   \]

2. **Calculate the denominator:**
   \[
   (-4)^5 = (-4) \times (-4) \times (-4) \times (-4) \times (-4) = -1024
   \]

3. **Simplify the fraction:**
   \[
   \frac{(-4)^3}{(-4)^5} = \frac{-64}{-1024} = \frac{1}{16}
   \]

4. **Now, divide by \((-4)^4\):**
   \[
   (-4)^4 = (-4) \times (-4) \times (-4) \times (-4) = 256
   \]
   \[
   \frac{1}{16} \div 256 = \frac{1}{16} \times \frac{1}{256} = \frac{1}{4096}
   \]

So, the final result is:

\[
\frac{(-4)^3}{(-4)^5} \div (-4)^4 = \frac{1}{4096}
\]

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. What is the value of \(\frac{(-3)^2}{(-3)^4} \div (-3)\)?
2. How do you simplify expressions with negative exponents?
3. What happens when you multiply two negative numbers?
4. How does the power of a negative number affect its sign?
5. Can you generalize the rule for \(\frac{a^m}{a^n}\) when \(m > n\)?

**Tip:** When dividing exponents with the same base, you can subtract the exponents directly: \(\frac{a^m}{a^n} = a^{m-n}\).

Learn how to solve the expression (-4)^3 : (-4)^5 / (-4)^4 involving exponents and negative numbers. This problem covers key concepts in exponents, negative number operations, and fraction simplification. Suitable for Grades 7-9.

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