91Ó°ÊÓ

Based on the step-by-step solution provided, answer the following question: **Question:** Prove Property 8 of Table 5.5, \(a^{-m} = \frac{1}{a^m}\), using Property 3 of Table 5.4, \((a^m)^n = a^{mn}\), and Property 7 of Table 5.5, \(a^0 = 1\). **Answer:** We began by applying Property 3 with \(n=0\), which gave us \((a^m)^0 = a^{m(0)}\), which simplified to \((a^m)^0 = a^0\). Next, we applied Property 7, which gave us \((a^m)^0 = 1\). We rewrote the fraction \(1/a^m\) as a product with an exponent: \(1 \cdot a^{-m} = \frac{1}{a^m}\). Then, we used Property 3 again to identify that \((a^m)^{-1} = a^{-m}\) and substituted this into the previous equation: \(1 \cdot (a^m)^{-1} = \frac{1}{a^m}\). This allowed us to prove Property 8 of Table 5.5: \(a^{-m} = \frac{1}{a^m}\).