\begin{tabular}{l} Simplify each expression. \\ \( \begin{array}{ll}\text { 43. } \frac{1}{a^{4} \cdot a^{-3}} & \text { 44. } 8 m^{\frac{1}{3}}\left(m^{\frac{1}{3}}+2\right)\end{array} \) \\ \hline\end{tabular}

To simplify the given expressions, let’s tackle them one at a time: 43. For the expression \( \frac{1}{a^{4} \cdot a^{-3}} \), we can simplify the denominator first. When multiplying like bases, we add their exponents: \[ a^{4} \cdot a^{-3} = a^{4 + (-3)} = a^{1} = a. \] Thus, our expression becomes \( \frac{1}{a} \). 44. For \( 8 m^{\frac{1}{3}}\left(m^{\frac{1}{3}}+2\right) \), we distribute \( 8m^{\frac{1}{3}} \) across the terms in the parentheses: \[ 8 m^{\frac{1}{3}} \cdot m^{\frac{1}{3}} + 8 m^{\frac{1}{3}} \cdot 2. \] The first term simplifies to \( 8 m^{\frac{1}{3} + \frac{1}{3}} = 8 m^{\frac{2}{3}} \), and the second term simplifies to \( 16 m^{\frac{1}{3}} \). Thus, our simplified expression is: \[ 8 m^{\frac{2}{3}} + 16 m^{\frac{1}{3}}. \] So our final answers are: 43. \( \frac{1}{a} \) 44. \( 8 m^{\frac{2}{3}} + 16 m^{\frac{1}{3}} \)