Wiskunde.net

67.
a.
(x³)⁴ = x³ ⋅ x³ ⋅ x³ ⋅ x³ = x^3+3+3+3 = x¹², dus (x³)⁴ = x^3x4 = x¹²
b.
(x⁶)³ = x⁶ ⋅ x⁶ ⋅ x⁶ = x⁶⁺⁶⁺⁶ = x¹⁸, dus (x⁶)³ = x^6x3 = x¹⁸

68.
a. a³⁵
b. p¹² ⋅ p¹² = p²⁴
c. p¹² + p¹² = 2p¹²
d. 5x ⋅ 3 ⋅ x²⁰ = 15x²¹
e. -2x⁶ - 3x⁶ = -5x⁶
f. 5x¹² - 7x⁸

69.
a.
(ab)⁴ = ab ⋅ ab ⋅ ab ⋅ ab = a ⋅ a ⋅ a ⋅ a ⋅ b ⋅ b ⋅ b ⋅ b = a⁴b⁴
b.
(3a)⁴ = 3a ⋅ 3a ⋅ 3a ⋅ 3a = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ a ⋅ a ⋅ a ⋅ a = 3⁴a⁴ = 81a⁴

70.
a. x⁷y⁷
b. 5³x³ = 125x³
c. (-10)²a² = 100a²
d. (-p)⁶ = (-1)⁶p⁶ = 1 ⋅ p⁶ = p⁶
e. (-3)³p³ = -27p³
f. - 2⁴q⁴ = -16q⁴

71.
a. (-3)⁴x⁸ = 81x⁸
b. a⁴b⁴c⁴
c. 8a³b³
d. (-3)³x³y³ = -27x³y³
e. 25x²y⁴
f. -a⁴b⁸

72.
a. (-3)³a⁶ ⋅ a¹⁵ = -27a⁶ ⋅ a¹⁵ = -27a²¹
b. (-2)⁴a⁴ ⋅ 9a⁶ = 16a⁴ ⋅ 9a⁶ = 144a¹⁰
c. p³q⁶ ⋅ p⁶q² = p⁹q⁸
d. 36x⁶ + 3x⁶ = 39x⁶
e. -3a⁸ ⋅ a⁹b³ = -3a¹⁷b³
f. -3a¹² + 4a¹² = a¹²

73.
a. 9x²y² + 5x²y² = 14x²y²
b. 25a⁶ - a⁶ = 24a⁶
c. 25a⁶ ⋅ a⁶ = 25a¹²
d. 3 ⋅ 8x⁶y³ - 125x³y³ = 24x⁶y³ - 125x³y³
e. -5x¹² - 4x¹² = -9x¹²
f. 625x¹² ⋅ 4x⁸ = 2500x²⁰

74.
a. 10^18-6 = 10¹²
b. 10^20-4 = 10¹⁶
c. 10^7-1 = 10⁶

75.
a. x^9-4 = x⁵
b. p^5-1 = p⁴
c. 1
d. -3x^10-5 = -3x⁵
e. 2y^4-3 = 2y¹ = 2y
f. 5k^25-5 = 5k²⁰

76.
a. x^8-6 = x²
b. kan niet
c. 14x
d. x⁸⁺⁶ = x¹⁴
e. 4/3 = 1 1/3
f. 48x⁸⁺⁶ = 48x¹⁴

77.
a. 3p
b. 2a³b
c. -3p

78.
a. a¹⁰ ⋅ a⁷ = a¹⁷
b. -4a²
c. a¹² / a⁵ = a^12-5 = a⁷
d. (-3)⁴a⁸ = 81a⁸
e. 3a⁸ - 4a⁸ = -a⁸
f. a¹⁵ / a¹⁵ = 1
g. 5⁴a⁸ = 625a⁸
h. -(-1)⁷a¹⁴ - a¹⁴ = - -a¹⁴ - a¹⁴ = a¹⁴ - a¹⁴ = 0
i. -a⁹ - a⁹ = -2a⁹

79.
a³ ⋅ 5a² = 5a⁵ ->
5a⁵ + 7a⁵ = 12a⁵ ->
12a⁵ / 6a = 2a⁴ ->
(2a⁴)⁴ = 16a¹⁶