1. Найдите значение выражения a^-7 * (a^5)^2 при a = 5.

1. $a^{-7} \cdot (a^5)^2 = a^{-7} \cdot a^{10} = a^{-7+10} = a^3$. При $a = 5$: $5^3 = 125$. 2. $a^{12} \cdot (a^{-4})^4 = a^{12} \cdot a^{-16} = a^{12-16} = a^{-4} = \frac{1}{a^4}$. При $a = -\frac{1}{2}$: $\frac{1}{(-1/2)^4} = \frac{1}{1/16} = 16$. 3. $\frac{(a^4)^4}{a^{14}} = \frac{a^{16}}{a^{14}} = a^{16-14} = a^2$. При $a = 6$: $6^2 = 36$. 4. $\frac{(a^3)^4}{a^9} = \frac{a^{12}}{a^9} = a^{12-9} = a^3$. При $a = 3$: $3^3 = 27$. 5. $\frac{(a^4)^5}{a^{18}} = \frac{a^{20}}{a^{18}} = a^{20-18} = a^2$. При $a = 3$: $3^2 = 9$. 6. $\frac{(a^7)^3}{a^{18}} = \frac{a^{21}}{a^{18}} = a^{21-18} = a^3$. При $a = 2$: $2^3 = 8$. 7. $\frac{1}{3^{-8}} \cdot \frac{1}{3^7} = 3^8 \cdot 3^{-7} = 3^{8-7} = 3^1 = 3$. 8. $\frac{1}{4^{-10}} \cdot \frac{1}{4^9} = 4^{10} \cdot 4^{-9} = 4^{10-9} = 4^1 = 4$.