Rewrite the expression in the form \( a x^{b} \) where \( a \) and \( b \) are numbers. Note that the variable, which does not have to be \( x \), should not be in a denominator and \( a \) is in front of the variable. \[ \sqrt[3]{\frac{27}{x^{-4}}} \]

To rewrite the given expression \( \sqrt[3]{\frac{27}{x^{-4}}} \), we start by simplifying the fraction inside the cube root: \[ \frac{27}{x^{-4}} = 27 \cdot x^{4} = 27x^{4} \] Now, we can take the cube root of this expression: \[ \sqrt[3]{27x^{4}} = \sqrt[3]{27} \cdot \sqrt[3]{x^{4}} \] Calculating the cube root of 27 gives us 3, and using the property of exponents, we find: \[ \sqrt[3]{x^{4}} = x^{\frac{4}{3}} \] Putting it all together, we have: \[ \sqrt[3]{27x^{4}} = 3 \cdot x^{\frac{4}{3}} \] Thus, the expression in the form \( a x^{b} \) is: \[ 3x^{\frac{4}{3}} \] Here, \( a = 3 \) and \( b = \frac{4}{3} \).