1. ¿Qué base debe tener un sistema de nume- ración para que la representación del núme ro 117 en dicho sistema sea 427 ?

Find, if possible, \( A B \) and \( B A \). If it is not possible, explain why. \[ A=\left[\begin{array}{rr}-4 & 4 \\ 0 & 1\end{array}\right] \quad B=\left[\begin{array}{rrrr}-5 & 0 & 4 & 1 \\ 3 & 0 & 1 & 9\end{array}\right] \]

Simplify the expression. \( \frac{2(5-4)^{3}-5 \cdot 9+7 \cdot 8}{9^{2}+8^{3}} \) \( \frac{2(5-4)^{3}-5 \cdot 9+7 \cdot 8}{9^{2}+8^{3}}=0.021922 \) (Round to the nearest thousandth.)

Simplify and add or subtract wherever possible. \( 2 \sqrt{32}-5 \sqrt{18}-2 \sqrt{27} \) The simplified form is (Type an exact answer, using radicals as needed.)

3). \( 9 \sqrt{12}+5 \sqrt{32}-\sqrt{72} \)

e) \( \sqrt{1+\frac{9}{16}}= \)