I. 1) 5³ + 2⁴ = 125 + 16 = 141
2) (-7)² - (-2)² = 49 - 4 = 45
3) 6 * (-5/6)² = 6 * 25/36 ≈ 4,16
II. 1) m⁴ * m⁶ = m¹⁰
2) x * x⁷ = x⁸
3) a² * a¹⁶ = a¹⁸
4) a⁶ * a⁶ = a¹²
5) y * y⁹ * y⁴ = y¹⁴
6) c³ * c² * c⁸ = c¹³
7) (m + 2n)¹⁰ * (m + 2n) = (m + 2n)¹¹
8) z⁵ * z² * z * z¹¹ = z¹⁹
III. 1) a¹⁵ : a⁴ = a¹¹
2) c⁹ : c = c⁸
3) b⁸ : b⁸ = 1
4) (a - b)¹² : (a - b)⁶ = (a - b)⁶
IV. 1) a⁵ * a¹⁴ = a¹⁹
2) a⁴ * a * a² = a⁷
3) a⁹ : a⁴ = a⁵
4) a⁴² : a¹⁰ = a³²
5) a¹⁴ : a¹² * a⁹ = a¹¹
6) a¹⁸ * a⁷ : a²³ = a²
V. 1) 3⁴ * 3⁵ = 3⁹ = 19683
2) 2⁵ * 2² = 2⁷ = 128
3) 5¹¹ * 5⁷ : 5¹⁵ = 5³ = 125
4) 29¹⁰ * 29⁶ : 29¹⁴ = 29² = 841
f'(x)=(7^x + sin(x) - 15x^4)'=7^x·ln7-cosx-15·4·x^3=7^x·ln7-cosx-60·x^3