1) a⁻⁸ ⋅ a¹²; 2) a⁷ ⋅ a⁻¹¹; 3) a⁻⁶ ⋅ a¹⁰; 4) a⁻³ : a⁵; 5) a⁻⁴ : a⁻¹²; 6) a¹⁷ ⋅ a⁻²³ : a⁻¹⁵; 1) 7⁵ ⋅ 7⁻⁷; 2) 10⁻¹² ⋅ 10¹⁵; 3) 5⁻¹² : 5⁻¹⁶;

Решение:

1. a⁻⁸ ⋅ a¹² = a^{-8 + 12} = a⁴
2. a⁷ ⋅ a⁻¹¹ = a^{7 + (-11)} = a^-4
3. a⁻⁶ ⋅ a¹⁰ = a^{-6 + 10} = a⁴
4. a⁻³ : a⁵ = a^{-3 - 5} = a^-8
5. a⁻⁴ : a⁻¹² = a^{-4 - (-12)} = a^{-4 + 12} = a⁸
6. a¹⁷ ⋅ a⁻²³ : a⁻¹⁵ = a^{17 + (-23)} : a⁻¹⁵ = a⁻⁶ : a⁻¹⁵ = a^{-6 - (-15)} = a^{-6 + 15} = a⁹
7. 7⁵ ⋅ 7⁻⁷ = 7^{5 + (-7)} = 7⁻²
8. 10⁻¹² ⋅ 10¹⁵ = 10^{-12 + 15} = 10³
9. 5⁻¹² : 5⁻¹⁶ = 5^{-12 - (-16)} = 5^{-12 + 16} = 5⁴

Ответ:

• 1) a⁴
• 2) a⁻⁴
• 3) a⁴
• 4) a⁻⁸
• 5) a⁸
• 6) a⁹
• 1) 7⁻²
• 2) 10³
• 3) 5⁴