№5. Свойство: (ab)" = a".br. (2·3)2 = (11·8)3 = (6·4)4 = (54·2)5 = (13·18)6 = (14·3)7 = (25·6)8 = (14·49)9: (16·12)10 (7·9)11 = (10·21)12 = (6·7)13 = (21·23) 14 = (44·55)15 = (78·17)16 =

№5. Свойство: $$(ab)^n = a^n \cdot b^n$$.

1. $$(2 \cdot 3)^2 = 2^2 \cdot 3^2 = 4 \cdot 9 = 36$$


2. $$(11 \cdot 8)^3 = 11^3 \cdot 8^3 = 1331 \cdot 512 = 681952$$


3. $$(6 \cdot 4)^4 = 6^4 \cdot 4^4 = 1296 \cdot 256 = 331776$$


4. $$(54 \cdot 2)^5 = 54^5 \cdot 2^5 = 459165024 \cdot 32 = 14693280768$$


5. $$(13 \cdot 18)^6 = 13^6 \cdot 18^6 = 4826809 \cdot 34012224 = 1,64172584901 \cdot 10^{13}$$


6. $$(14 \cdot 3)^7 = 14^7 \cdot 3^7 = 105413504 \cdot 2187 = 2,3054600228 \cdot 10^{11}$$


7. $$(25 \cdot 6)^8 = 25^8 \cdot 6^8 = 152587890625 \cdot 1679616 = 2,562890625 \cdot 10^{14}$$


8. $$(14 \cdot 49)^9 = 14^9 \cdot 49^9 = 5159780352 \cdot 40353607502 = 2,08108303651 \cdot 10^{19}$$


9. $$(16 \cdot 12)^{10} = 16^{10} \cdot 12^{10} = 1099511627776 \cdot 61917364224 = 6,80796426755 \cdot 10^{22}$$


10. $$(7 \cdot 9)^{11} = 7^{11} \cdot 9^{11} = 1977326743 \cdot 31381059609 = 6,20386770287 \cdot 10^{19}$$


11. $$(10 \cdot 21)^{12} = 10^{12} \cdot 21^{12} = 1000000000000 \cdot 7979226629761 = 7,97922662976 \cdot 10^{24}$$


12. $$(6 \cdot 7)^{13} = 6^{13} \cdot 7^{13} = 13060694016 \cdot 96889010407 = 1,26533488106 \cdot 10^{23}$$


13. $$(21 \cdot 23)^{14} = 21^{14} \cdot 23^{14} = 30463290778025 \cdot 2,00476122319323 \cdot 10^{19} = 6,10728314582 \cdot 10^{26}$$


14. $$(44 \cdot 55)^{15} = 44^{15} \cdot 55^{15} = 1,793343555106191 \cdot 10^{25} \cdot 9,52711289127041 \cdot 10^{25} = 1,70853049236 \cdot 10^{51}$$


15. $$(78 \cdot 17)^{16} = 78^{16} \cdot 17^{16} = 1,543168306106596 \cdot 10^{29} \cdot 8,352061485121 \cdot 10^{19} = 1,28880806521 \cdot 10^{49}$$

Ответ: 1) $$36$$; 2) $$681952$$; 3) $$331776$$; 4) $$14693280768$$; 5) $$1,64172584901 \cdot 10^{13}$$; 6) $$2,3054600228 \cdot 10^{11}$$; 7) $$2,562890625 \cdot 10^{14}$$; 8) $$2,08108303651 \cdot 10^{19}$$; 9) $$6,80796426755 \cdot 10^{22}$$; 10) $$6,20386770287 \cdot 10^{19}$$; 11) $$7,97922662976 \cdot 10^{24}$$; 12) $$1,26533488106 \cdot 10^{23}$$; 13) $$6,10728314582 \cdot 10^{26}$$; 14) $$1,70853049236 \cdot 10^{51}$$; 15) $$1,28880806521 \cdot 10^{49}$$