1) Simplify. Express your answer using positive exponents. \( \frac{8 f^{-2} \cdot 6 f}{2 f^{8}} \)

To simplify the expression \( \frac{8 f^{-2} \cdot 6 f}{2 f^{8}} \), we first simplify the coefficients and then the powers of \( f \). Start with the coefficients: \( \frac{8 \cdot 6}{2} = \frac{48}{2} = 24 \). Now for the \( f \) terms: Combine the exponents in the numerator: \( f^{-2} \cdot f = f^{-2 + 1} = f^{-1} \). So now we have: \[ \frac{24 f^{-1}}{f^8} = 24 \cdot f^{-1 - 8} = 24 f^{-9}. \] To express it using positive exponents, we write: \[ 24 f^{-9} = \frac{24}{f^9}. \] Thus, the simplified form is: \(\frac{24}{f^9}\).