The expression to rewrite is:

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

Step-by-step solution:

1. Recall the rule for negative exponents: $a^{-n} = \frac{1}{a^n}$

2. Applying this rule to $4^{-3}$: $4^{-3} = \frac{1}{4^3}$

3. Substitute $\frac{1}{4^3}$ back into the denominator: $\frac{1}{4^{-3}} = \frac{1}{\frac{1}{4^3}}$

4. Simplify the fraction: $\frac{1}{\frac{1}{4^3}} = 4^3$

5. Compute $4^3$: $4^3 = 4 \cdot 4 \cdot 4 = 64$

Final Answer:

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

Would you like further clarification or a deeper explanation? 😊

Related Questions:

1. What is the general rule for rewriting negative exponents?
2. How can you simplify an expression with exponents in both the numerator and denominator?
3. What does it mean for a number to have a negative exponent?
4. Can you express $64$ as a power of $2$?
5. How would the answer change if the base was a fraction, like $\frac{1}{2}^{-3}$?

Tip:

Always simplify negative exponents by flipping the base (reciprocal) first. This makes computations more intuitive!