¡Claro! Vamos a resolver cada uno de estos ejercicios utilizando la propiedad de la división de potencias de igual base: [tex]$\frac{a^n}{a^m} = a^{n-m}$[/tex].
1. [tex]\(\frac{5^2}{5} \)[/tex]
[tex]\[ \frac{5^2}{5} = 5^{2-1} = 5^1 = 5 \][/tex]
2. [tex]\(\frac{3^3}{3^2} \)[/tex]
[tex]\[ \frac{3^3}{3^2} = 3^{3-2} = 3^1 = 3 \][/tex]
3. [tex]\(\frac{2^4}{2^2} \)[/tex]
[tex]\[ \frac{2^4}{2^2} = 2^{4-2} = 2^2 = 4 \][/tex]
4. [tex]\(\frac{8^7}{8^5} \)[/tex]
[tex]\[ \frac{8^7}{8^5} = 8^{7-5} = 8^2 = 64 \][/tex]
6. [tex]\(\frac{4^9}{4^6} \)[/tex]
[tex]\[ \frac{4^9}{4^6} = 4^{9-6} = 4^3 = 64 \][/tex]
7. [tex]\(\frac{10^3}{10^1} \)[/tex]
[tex]\[ \frac{10^3}{10^1} = 10^{3-1} = 10^2 = 100 \][/tex]
8. [tex]\(\frac{6^{13}}{6^{10}} \)[/tex]
[tex]\[ \frac{6^{13}}{6^{10}} = 6^{13-10} = 6^3 = 216 \][/tex]
9. [tex]\(\frac{7^5}{7^2} \)[/tex]
[tex]\[ \frac{7^5}{7^2} = 7^{5-2} = 7^3 = 343 \][/tex]
11. [tex]\(\frac{11^{16}}{11^{15}} \)[/tex]
[tex]\[ \frac{11^{16}}{11^{15}} = 11^{16-15} = 11^1 = 11 \][/tex]
12. [tex]\(\frac{2^{17}}{2^9} \)[/tex]
[tex]\[ \frac{2^{17}}{2^9} = 2^{17-9} = 2^8 = 256 \][/tex]
13. [tex]\(\frac{13^3}{13^1} \)[/tex]
[tex]\[ \frac{13^3}{13^1} = 13^{3-1} = 13^2 = 169 \][/tex]
14. [tex]\(\frac{3^{21}}{3^{17}} \)[/tex]
[tex]\[ \frac{3^{21}}{3^{17}} = 3^{21-17} = 3^4 = 81 \][/tex]
Por lo tanto, los resultados son:
1. [tex]\(5\)[/tex]
2. [tex]\(3\)[/tex]
3. [tex]\(4\)[/tex]
4. [tex]\(64\)[/tex]
6. [tex]\(64\)[/tex]
7. [tex]\(100\)[/tex]
8. [tex]\(216\)[/tex]
9. [tex]\(343\)[/tex]
11. [tex]\(11\)[/tex]
12. [tex]\(256\)[/tex]
13. [tex]\(169\)[/tex]
14. [tex]\(81\)[/tex]
