\( \left. \begin{array} { l } { \operatorname { let } g ( x ) = ( 3 x - 1 ) ^ { 2 } - ( 2 x - 3 ) ^ { 2 } } \\ { g ( x ) } \end{array} \right. \)

Calaula las saguientes determinantes \( \begin{array}{ll}\text { a) }\left|\begin{array}{cc}-8 & 9 \\ -1 & 20\end{array}\right| & \text { b }\left|\begin{array}{ll}2 & \frac{1}{3} \\ \frac{1}{2} & -1\end{array}\right| \text { c) }\left|\begin{array}{cc}5 & -a \\ 2 a & 4 a^{2}\end{array}\right|\end{array} \)

e) \( \sqrt[2]{2} \cdot \sqrt[2]{18}= \)

Aplica el método de fracciones parciales a la función: \( \frac{x^2 + 2}{(x-1)(x+3)} \)

a) \( \left(3^{6}\right)^{7} \cdot 3^{2}: 3^{41}-5^{2}= \) c) \( \left[\left(2^{2}\right)^{3}\right]^{3}:\left(2^{3}\right)^{5}= \) e) \( 4^{3} \cdot\left(4^{5}\right)^{4}:\left(4^{3}\right)^{7}-2^{4}= \) g) \( \left[\left(5^{3}\right)^{12}:\left(5^{2}\right)^{17}-25\right]: 5= \) i) \( \left.2^{6}+10 \cdot\left[3 \cdot 3^{3}-\left(3^{4}\right)^{3}: 3^{11}\right)\right]= \)

d) \( \frac{3^{4}: 3}{3^{2}}= \)