b) \( \frac{\left(3^{2}\right)^{7} \cdot\left(3^{3}\right)^{5}}{3^{27}}= \)

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.)

\( 1 \leftarrow \quad \) Determine whether \( B \) is the inverse of \( A \). \( A=\left[\begin{array}{rr}3 & -7 \\ -2 & 5\end{array}\right], \quad B=\left[\begin{array}{ll}5 & 7 \\ 2 & 3\end{array}\right] \)

Simplify. \( [32-(15+5) \div 4]-[56 \div(8-1)]^{\prime} \) \( [32-(15+5) \div 4]-[56 \div(8-1)]=\square \)

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

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