\( \begin{array}{l}\text { Simplify the expression. Assume that variables represent } \\ \text { non-zero real numbers. }\end{array} \) \( \begin{array}{ll}\frac{6 a^{5}\left(a^{-2}\right)^{6}}{\left(a^{-1}\right)^{-3}} & \frac{6 a^{5}\left(a^{-2}\right)^{6}}{\left(a^{-1}\right)^{-3}}=\square \\ \text { (Simplify your answer. Type in exponenti. } \\ \text { notation. Type positive exponents.) }\end{array} \)

Eelow is the graph of \( y=x^{2} \). nandorm it to make it the graph of \( y=3(x+1)^{2}+4 \).

a) \( \left\{\begin{aligned}-\frac{1}{9} x-\frac{3}{5} y & =\frac{7}{45} \\ \frac{1}{8} x+\frac{1}{4} y & =\frac{1}{4}\end{aligned}\right. \)

Perform the subtraction: \( (6y^{4} - 3y^{2} + 1) - (2y^{4} + 5y^{2} - 8) \)

EJERCIADOS EN EL AULA. \( y=-x^{2}+4 x+6 \) analizarla desde \( x=0, a x=+4 \)

Calcula los siguientes determinantes utilizando el desarrollo por los elementos de la línea más conveniênte: \( \begin{array}{ll}\text { a) }\left|\begin{array}{ccc}2 & 3 & -1 \\ 5 & 0 & -7 \\ 0 & 14 & 0\end{array}\right| & \text { b) }\left|\begin{array}{ccc}-1 & a & -a \\ 0 & 2 & -3 \\ 1 & a & 2\end{array}\right| \\ \text { c) }\left|\begin{array}{cccc}2 & 3 & -1 & 0 \\ 6 & 4 & -3 & 5 \\ 2 & -1 & 2 a & -3 \\ 0 & 2 a & 0 & a^{2}\end{array}\right| & \text { d) }\left|\begin{array}{cccc}-11 & 2 & 1 & -2 \\ 0 & 1 & -1 & 8 \\ 1 & 0 & 1 & -1 \\ 0 & 3 & 1 & 4\end{array}\right|\end{array} \)