Üslü sayılarla ilgili çözümlü sorular
| Soru1: | |
| `2^{3}.2^{5}.2^{7}=?` | |
| Çözüm: | |
| `2^{3}.2^{5}.2^{7}=2^{3+5+7}=2^{15}` | |
| Soru2: | |
| `\frac{5^{7}.5^{4}}{5^{2}}=?` | |
| `\frac{5^{7}.5^{4}}{5^{2}}=\frac{5^{7+4}}{5^{2}}=\frac{5^{11}}{5^{2}}=5^{11-2}=5^{9}` | |
| Soru 3: | |
| `\frac{-2^{3}+(-2)^{3}}{-2^{2}-(-2)^{5}}=?` | |
| Çözüm : | |
| `\frac{-2^{3}+(-2)^{3}}{-2^{2}-(-2)^{5}}=\frac{-8+(-8)}{-4-(-32)}=\frac{-16}{28}=\frac{-4}{7}` | |
| Özellik: | |
| `a^{-n}=\frac{1}{a^{n}},` | |
| `(\frac{a}{b})^{-n}=(\frac{b}{a})^{n}` | |
| Soru 4: | |
| `\frac{(\frac{1}{2})^{-3}+3^{-1}}{(\frac{3}{2})^{-2}}=?` | |
| Çözüm : | |
| `\frac{(\frac{1}{2})^{-3}+3^{-1}}{(\frac{3}{2})^{-2}}=\frac{2^{3}+(\frac{1}{3})}{(\frac{2}{3})^{2}}=\frac{8+(\frac{1}{3})}{\frac{4}{9}}=\frac{\frac{25}{3}}{\frac{4}{9}}=\frac{25}{3}.\frac{9}{4}=\frac{225}{12}=\frac{75}{4}` | |