7. a)
(3² * 5ⁿ + 4² * 5ⁿ) : 5ⁿ⁺² = 1
5ⁿ(3² + 4²) : 5ⁿ * 5² = 1
(9 + 16) : 25 = 1
25 : 25 = 1
1 = 1
b)
18 * 7ⁿ - 11 * 7ⁿ = 7ⁿ⁺¹
7ⁿ(18 - 11) = 7ⁿ * 7¹ | : 7ⁿ
7 = 7
8. a)
5²³ : 5²¹ + 2⁶ * 2⁴ - (2²)⁵ =
5² + 2¹⁰ - 2¹⁰ =
5² = 25
b)
5⁴ * 3⁴ - (15²)² =
5⁴ * 3⁴ - 15⁴ =
5⁴ * 3⁴ - 3⁴ * 5⁴ =
0
c)
(16 - 12)⁴ : 4³ - 3⁷ : (3² - 6)⁷ =
4⁴ : 4³ - 3⁷ : (9 - 6)⁷ =
1 - 3⁷ : 3⁷ =
1 - 1 =
0
9.
(2⁶ * 4³ * 8²)⁵ : 16³ =
[2⁶ * (2²)² * (2³)²]⁵ : (2⁴)³ =
(2⁶ * 2⁴ * 2⁶)⁵ : 2¹² =
(2¹⁶)⁵ : 2¹² =
2⁸⁰ : 2¹² =
2⁶⁸
