The given mathematical expression is:

$4^{-3}$

To simplify this, we use the negative exponent rule:

$a^{-b} = \frac{1}{a^b}$

Applying this rule:

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

Now, calculating $4^3$:

$4^3 = 4 \times 4 \times 4 = 64$

Thus:

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

Final Answer:

$\frac{1}{64}$

Would you like a more detailed explanation or have any questions?

Related Questions:

1. What is the general rule for negative exponents?
2. How do you simplify expressions with multiple negative exponents?
3. How do you express $\frac{1}{64}$ as a decimal?
4. What is the difference between negative exponents and fractional exponents?
5. How do you simplify expressions with different bases but the same exponent?

Tip:

When dealing with negative exponents, always remember that they indicate the reciprocal of the base raised to the positive exponent.