Simplify. Write your answers without exponents. \[ \left(\frac{1}{8}\right)^{-\frac{3}{2}}=\square \]

To simplify \(\left(\frac{1}{8}\right)^{-\frac{3}{2}}\), we can start by remembering that a negative exponent indicates a reciprocal. Thus, \[ \left(\frac{1}{8}\right)^{-\frac{3}{2}} = \left(\frac{8}{1}\right)^{\frac{3}{2}} = 8^{\frac{3}{2}}. \] Next, we can break down \(8\) into its prime factors: \[ 8 = 2^3. \] Now substituting this into our expression gives us: \[ 8^{\frac{3}{2}} = (2^3)^{\frac{3}{2}} = 2^{3 \cdot \frac{3}{2}} = 2^{\frac{9}{2}}. \] To simplify further, we can express \(2^{\frac{9}{2}}\) in radical form: \[ 2^{\frac{9}{2}} = 2^4 \cdot 2^{\frac{1}{2}} = 16 \cdot \sqrt{2}. \] Thus, the final simplified answer is: \[ \left(\frac{1}{8}\right)^{-\frac{3}{2}} = 16\sqrt{2}. \]