The problem asks to find an equivalent expression for $4^{-3}$.

1. Problem Description

The problem asks to find an equivalent expression for $4^{-3}$.

2. Solution Steps

To solve this problem, we need to remember the rule for negative exponents:

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

Applying this rule to the given expression:

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

Now we evaluate $4^3$:

$4^3 = 4 \times 4 \times 4 = 16 \times 4 = 64$

Therefore,

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

The options are:

A. $-4^3 = -64$

B. $\frac{1}{4^3} = \frac{1}{64}$

C. $\frac{1^3}{4} = \frac{1}{4}$

Therefore, option B is the equivalent expression.

3. Final Answer

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