The expression given is $4^{-3}$.

To simplify this:

1. The negative exponent rule states that $a^{-b} = \frac{1}{a^b}$, so: $4^{-3} = \frac{1}{4^3}$

2. Now, calculate $4^3$: $4^3 = 4 \times 4 \times 4 = 64$

Thus, the equivalent expression is: $4^{-3} = \frac{1}{64}$

Would you like further details on the process or have any questions?

Here are 5 related questions to expand on this:

1. How do you simplify expressions with negative exponents in general?
2. Can you explain how to simplify $a^{-n} \times a^n$?
3. How would you handle an expression like $(2^3)^{-2}$?
4. What happens when the base of the exponent is a fraction, such as $\left(\frac{1}{2}\right)^{-3}$?
5. How can negative exponents be used to represent very small numbers?

Tip: Whenever you encounter a negative exponent, remember that it flips the base into its reciprocal, making it a fraction.