b \( (x+2)^{2}-x^{2}=0 \) d \( (2 x-1)^{2}=(2-3 x)^{2} \)

Three-fifths of Jesse Black's inventory was destroyed by fire. He sold the remaining part, which was slightly damaged, for two-thirds of its value and received \( \$ 3400 \). (a) What was the value of the destroyed part of the inventory? (b) What was the value of the inventory before the fire? (a) The value is \( \$ \square \). (Round to the nearest cent as needed.)

a) \( x+y=2 \) b) \( x+x-y=4+y \)

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

\begin{tabular}{l|l}\( \begin{array}{l}\text { Simplify the expression so that no negative exponents } \\ \text { appear in the final result. Assume all variables represent } \\ \text { nonzero real numbers. }\end{array} \) & \( \begin{array}{l}\left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}=\square \\ \\ \left(4 a^{-2}\right)^{4}\left(a^{4}\right)^{-3}\end{array} \) \\ exponents only.) \end{tabular}

\( 1 \leftarrow \) Show that \( A I=I A=A \). \( A=\left[\begin{array}{rr}1 & 8 \\ -2 & 2\end{array}\right] \)