Para resolver las siguientes fracciones utilizando las propiedades de los exponentes, aplicamos la propiedad [tex]\(\frac{a^m}{a^n} = a^{m-n}\)[/tex] y simplificamos cada expresión paso a paso.
1) [tex]\(\frac{5^2}{5}\)[/tex]:
[tex]\[ \frac{5^2}{5^1} = 5^{2-1} = 5^1 = 5 \][/tex]
Valor: 5
2) [tex]\(\frac{3^3}{3^2}\)[/tex]:
[tex]\[ \frac{3^3}{3^2} = 3^{3-2} = 3^1 = 3 \][/tex]
Valor: 3
6) [tex]\(\frac{4^9}{4^6}\)[/tex]:
[tex]\[ \frac{4^9}{4^6} = 4^{9-6} = 4^3 = 64 \][/tex]
Valor: 64
7) [tex]\(\frac{10^3}{10^1}\)[/tex]:
[tex]\[ \frac{10^3}{10^1} = 10^{3-1} = 10^2 = 100 \][/tex]
Valor: 100
3) [tex]\(\frac{2^4}{2^2}\)[/tex]:
[tex]\[ \frac{2^4}{2^2} = 2^{4-2} = 2^2 = 4 \][/tex]
Valor: 4
4) [tex]\(\frac{8^7}{8^5}\)[/tex]:
[tex]\[ \frac{8^7}{8^5} = 8^{7-5} = 8^2 = 64 \][/tex]
Valor: 64
5) [tex]\(\frac{12^6}{12^5}\)[/tex]:
[tex]\[ \frac{12^6}{12^5} = 12^{6-5} = 12^1 = 12 \][/tex]
Valor: 12
8) [tex]\(\frac{6^{13}}{6^{10}}\)[/tex]:
[tex]\[ \frac{6^{13}}{6^{10}} = 6^{13-10} = 6^3 = 216 \][/tex]
Valor: 216
9) [tex]\(\frac{7^5}{7^2}\)[/tex]:
[tex]\[ \frac{7^5}{7^2} = 7^{5-2} = 7^3 = 343 \][/tex]
Valor: 343
10) [tex]\(\frac{9^{31}}{9^{73}}\)[/tex]:
[tex]\[ \frac{9^{31}}{9^{73}} = 9^{31-73} = 9^{-42} = \frac{1}{9^{42}} \][/tex]
Valor: [tex]\( 8.352463828623922 \times 10^{-41} \)[/tex]
11) [tex]\(\frac{11^{16}}{11^{15}}\)[/tex]:
[tex]\[ \frac{11^{16}}{11^{15}} = 11^{16-15} = 11^1 = 11 \][/tex]
Valor: 11
12) [tex]\(\frac{2^{17}}{2^9}\)[/tex]:
[tex]\[ \frac{2^{17}}{2^9} = 2^{17-9} = 2^8 = 256 \][/tex]
Valor: 256
13) [tex]\(\frac{13^3}{13^1}\)[/tex]:
[tex]\[ \frac{13^3}{13^1} = 13^{3-1} = 13^2 = 169 \][/tex]
Valor: 169
14) [tex]\(\frac{3^{21}}{3^{17}}\)[/tex]:
[tex]\[ \frac{3^{21}}{3^{17}} = 3^{21-17} = 3^4 = 81 \][/tex]
Valor: 81
15) [tex]\(\frac{14^{11}}{14^{11}}\)[/tex]:
[tex]\[ \frac{14^{11}}{14^{11}} = 14^{11-11} = 14^0 = 1 \][/tex]
Valor: 1
