№4. Свойство: (а")m = anm. (12)5 = (23)7 = (37)9 = (47)2 = (55)5 = (69)3 = (74)3 = (87)9 = (910)11 = (106)2 = (112)4 = (1223)2 = (136)8 = (149)4 = (152)7 =

№4. Свойство: $$(a^n)^m = a^{n \cdot m}$$.

1. $$(1^2)^5 = 1^{2 \cdot 5} = 1^{10} = 1$$


2. $$(2^3)^7 = 2^{3 \cdot 7} = 2^{21} = 2097152$$


3. $$(3^7)^9 = 3^{7 \cdot 9} = 3^{63} = 4,45607826475 \cdot 10^{30}$$


4. $$(4^7)^2 = 4^{7 \cdot 2} = 4^{14} = 268435456$$


5. $$(5^5)^5 = 5^{5 \cdot 5} = 5^{25} = 2,98023223877 \cdot 10^{17}$$


6. $$(6^9)^3 = 6^{9 \cdot 3} = 6^{27} = 5,575238470507953 \cdot 10^{20}$$


7. $$(7^4)^3 = 7^{4 \cdot 3} = 7^{12} = 13841287201$$


8. $$(8^7)^9 = 8^{7 \cdot 9} = 8^{63} = 4,144364156454619 \cdot 10^{56}$$


9. $$(9^{10})^{11} = 9^{10 \cdot 11} = 9^{110} = 2,97547266051204 \cdot 10^{104}$$


10. $$(10^6)^2 = 10^{6 \cdot 2} = 10^{12} = 1000000000000$$


11. $$(11^2)^4 = 11^{2 \cdot 4} = 11^{8} = 214358881$$


12. $$(12^{23})^2 = 12^{23 \cdot 2} = 12^{46} = 1,1916733461331335 \cdot 10^{49}$$


13. $$(13^6)^8 = 13^{6 \cdot 8} = 13^{48} = 2,512025419047869 \cdot 10^{53}$$


14. $$(14^9)^4 = 14^{9 \cdot 4} = 14^{36} = 1,1367349833325819 \cdot 10^{40}$$


15. $$(15^2)^7 = 15^{2 \cdot 7} = 15^{14} = 2,918781359363875 \cdot 10^{16}$$

Ответ: 1) $$1^{10} = 1$$; 2) $$2^{21} = 2097152$$; 3) $$3^{63} = 4,45607826475 \cdot 10^{30}$$; 4) $$4^{14} = 268435456$$; 5) $$5^{25} = 2,98023223877 \cdot 10^{17}$$; 6) $$6^{27} = 5,575238470507953 \cdot 10^{20}$$; 7) $$7^{12} = 13841287201$$; 8) $$8^{63} = 4,144364156454619 \cdot 10^{56}$$; 9) $$9^{110} = 2,97547266051204 \cdot 10^{104}$$; 10) $$10^{12} = 1000000000000$$; 11) $$11^{8} = 214358881$$; 12) $$12^{46} = 1,1916733461331335 \cdot 10^{49}$$; 13) $$13^{48} = 2,512025419047869 \cdot 10^{53}$$; 14) $$14^{36} = 1,1367349833325819 \cdot 10^{40}$$; 15) $$15^{14} = 2,918781359363875 \cdot 10^{16}$$