№3. Свойство: a": am = an-m. 15:12 = 5-2=43 49:42 = 9-2=47 24:23 = 4-3=2+ 511:57 = 11-7=54 38:33 = 8-3=5=35 721:78 = 21-8=714 84:81 = 4-1=3=89 1033 = 1019 = 118 = 134 = 142 = 124 = 13 14 15

Выполним вычисления, используя свойство деления степеней с одинаковым основанием $$a^n:a^m = a^{n-m}$$.

• $$15:12 = 5 - 2 = 5^3$$
• $$49:42 = 9 - 2 = 4^7$$
• $$24:23 = 4 - 3 = 2^1$$
• $$511:57 = 11 - 7 = 5^4$$
• $$38:33 = 8 - 3 = 5 = 3^5$$
• $$721:78 = 21 - 8 = 7^{13}$$
• $$84:81 = 4 - 1 = 3 = 8^3$$

• $$\frac{10^{33}}{10^{19}} = 10^{33-19} = 10^{14}$$
• $$\frac{11^9}{11^8} = 11^{9-8} = 11^1 = 11$$
• $$\frac{12^6}{12^4} = 12^{6-4} = 12^2$$
• $$\frac{13^4}{13} = 13^{4-1} = 13^3$$
• $$\frac{14^2}{14} = 14^{2-1} = 14^1 = 14$$
• $$\frac{15^{10}}{15} = 15^{10-1} = 15^9$$

Ответ:

• $$15:12 = 5^3$$
• $$49:42 = 4^7$$
• $$24:23 = 2^1$$
• $$511:57 = 5^4$$
• $$38:33 = 3^5$$
• $$721:78 = 7^{13}$$
• $$84:81 = 8^3$$
• $$\frac{10^{33}}{10^{19}} = 10^{14}$$
• $$\frac{11^9}{11^8} = 11$$
• $$\frac{12^6}{12^4} = 12^2$$
• $$\frac{13^4}{13} = 13^3$$
• $$\frac{14^2}{14} = 14$$
• $$\frac{15^{10}}{15} = 15^9$$