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: $\frac{a^m}{a^n} = a^{m-n}$.