\( m^{-\frac{1}{4}}=27 m^{-1} \) Find the value of \( m \).

To solve the equation \( m^{-\frac{1}{4}} = 27 m^{-1} \), we can start by rewriting the equation in a more manageable form. First, rewrite \( m^{-1} \) as \( \frac{1}{m} \): \[ m^{-\frac{1}{4}} = \frac{27}{m} \] Now, multiplying both sides by \( m \) (assuming \( m \neq 0 \)) gives us: \[ m^{\frac{3}{4}} = 27 \] Next, we need to raise both sides to the power of \( \frac{4}{3} \): \[ m = 27^{\frac{4}{3}} \] Calculating \( 27^{\frac{4}{3}} \), we know that \( 27 = 3^3 \), so: \[ 27^{\frac{4}{3}} = (3^3)^{\frac{4}{3}} = 3^{3 \cdot \frac{4}{3}} = 3^4 = 81 \] Thus, the value of \( m \) is: \[ \boxed{81} \]