Solve for \( M \). Assume that all other variables are nonzero. \( Q=\frac{2 \text { twM }^{2}}{3 c} \) \( M=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.

\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}

Calcule todos los valores de a para los cuales la matriz \( A=\left[\begin{array}{lll}a & 0 & 4 \\ 1 & 1 & a \\ a & 1 & 2\end{array}\right] \) es no invertit

Rewrite the following without an exponent \[ (-7)^{-2} \]

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

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.)