Simplify the following expression and express the final answer with positive exponents: \[ (4 c)^{-3} \] \( \sqrt[3]{4 c} \) \( \frac{1}{(4 c)^{3}} \) \( -64 c^{3} \) \( \frac{1}{\sqrt[3]{4 c}} \) \( \frac{1}{64 c^{3}} \)

We begin with the expression \[ (4c)^{-3}. \] A negative exponent means we take the reciprocal of the base raised to the corresponding positive exponent. Therefore, \[ (4c)^{-3} = \frac{1}{(4c)^3}. \] Next, we simplify the denominator by applying the exponent to both factors: \[ (4c)^3 = 4^3 \cdot c^3 = 64 c^3. \] Substituting this back into the expression, we get: \[ \frac{1}{(4c)^3} = \frac{1}{64 c^3}. \] Thus, the simplified expression with positive exponents is \[ \frac{1}{64 c^3}. \]