The problem requires evaluating $4^{-3}$ and expressing the result as a fraction or whole number without exponents.

Step-by-Step Solution:

1. Understanding Negative Exponents:
   A negative exponent means the reciprocal of the base raised to the positive exponent:
   $a^{-n} = \frac{1}{a^n}$

2. Apply the Rule:
   Here, $4^{-3}$ becomes:
   $4^{-3} = \frac{1}{4^3}$

3. Evaluate $4^3$:
   $4^3$ means multiplying $4$ three times:
   $4^3 = 4 \times 4 \times 4 = 64$

4. Simplify:
   Substituting back, we get:
   $4^{-3} = \frac{1}{64}$

Final Answer:

$4^{-3} = \frac{1}{64}$

Would you like further clarification on exponents or related examples?

Related Questions:

1. What is the value of $5^{-2}$?
2. How do you simplify $2^{-4}$?
3. What is $10^{-3}$ as a fraction?
4. How do you convert $3^{-2}$ to a fraction?
5. What is the reciprocal of $8^2$?

Tip: To simplify negative exponents, always start by flipping the base to its reciprocal and changing the exponent to positive!