Simplify. Write your answers without exponents. \[ \begin{array}{l}25^{-\frac{3}{2}}=\square \\ \left(\frac{1}{8}\right)^{-\frac{4}{3}}=\square\end{array} \]

For the first expression, \( 25^{-\frac{3}{2}} \) can be rewritten as \( \frac{1}{25^{\frac{3}{2}}} \). Since \( 25 \) is \( 5^2 \), we have \( 25^{\frac{3}{2}} = (5^2)^{\frac{3}{2}} = 5^{3} = 125 \). Therefore, \( 25^{-\frac{3}{2}} = \frac{1}{125} \). For the second expression, \( \left(\frac{1}{8}\right)^{-\frac{4}{3}} \) can be expressed as \( \left(8\right)^{\frac{4}{3}} \) because of the negative exponent. Recognizing that \( 8 = 2^3 \), we find \( 8^{\frac{4}{3}} = (2^3)^{\frac{4}{3}} = 2^4 = 16 \). Thus, \( \left(\frac{1}{8}\right)^{-\frac{4}{3}} = 16 \). So, the answers are: \[ \begin{array}{l} \frac{1}{125} \\ 16 \end{array} \]