№4. Свойство: (an)m = arm. (12)5 = (47)2 = (74)3 = (106)2 = (136) = (23)7 = (37)9 = (55)5 = (69)3 = (87)9 = (112)4 = (149)4 = (910)11 = (1223)2 = (152)7 =

Для решения данных примеров необходимо воспользоваться свойством степеней: $$(a^n)^m = a^{n \cdot m}$$.

1. $$(1^2)^5 = 1^{2 \cdot 5} = 1^{10} = 1$$
2. $$(4^7)^2 = 4^{7 \cdot 2} = 4^{14} = 268435456$$
3. $$(7^4)^3 = 7^{4 \cdot 3} = 7^{12} = 13841287201$$
4. $$(10^6)^2 = 10^{6 \cdot 2} = 10^{12} = 1000000000000$$
5. $$(13^6)^8 = 13^{6 \cdot 8} = 13^{48} = 1.4259927780718675e+53$$
6. $$(2^3)^7 = 2^{3 \cdot 7} = 2^{21} = 2097152$$
7. $$(3^7)^9 = 3^{7 \cdot 9} = 3^{63} = 4.423836737012672e+30$$
8. $$(5^5)^5 = 5^{5 \cdot 5} = 5^{25} = 2.9802322387695312e+17$$
9. $$(6^9)^3 = 6^{9 \cdot 3} = 6^{27} = 8.557659601147846e+20$$
10. $$(8^7)^9 = 8^{7 \cdot 9} = 8^{63} = 3.022314549036573e+56$$
11. $$(9^{10})^{11} = 9^{10 \cdot 11} = 9^{110} = 2.436518486251727e+105$$
12. $$(11^2)^4 = 11^{2 \cdot 4} = 11^8 = 214358881$$
13. $$(12^{23})^2 = 12^{23 \cdot 2} = 12^{46} = 2.821109907456e+49$$
14. $$(14^9)^4 = 14^{9 \cdot 4} = 14^{36} = 1.3389382370974974e+41$$
15. $$(15^2)^7 = 15^{2 \cdot 7} = 15^{14} = 2.9187813595520018e+16$$

Ответ: 1; 268435456; 13841287201; 1000000000000; 1.4259927780718675e+53; 2097152; 4.423836737012672e+30; 2.9802322387695312e+17; 8.557659601147846e+20; 3.022314549036573e+56; 2.436518486251727e+105; 214358881; 2.821109907456e+49; 1.3389382370974974e+41; 2.9187813595520018e+16.