Odpowiedź:
a)
4^10 : 2^4 * (-0,5)² = (2²)^10 : 2^4 * (-1/2)² = 2^20 : 2^4 * 2^-2 = 2^16 * 2^-2 = 2^14
b)
[(-2)^5]^-2 * 2^7 = (-2)^-10 * 2^7 = 2^-10 * 2^7 = 2^-3
c)
(3³)^4 : 9³ * (-3)^0 = 3^12 : (3²)³ * 3^0 = 3^12 : 3^6 * 1 = 3^6
d)
∛(7√7) = ∛7^(1 + 1/2) = ∛7^3/2 = 7^(1 2/3)^1/3 = 7^(5/3*1/3) = 7^5/9
e)
2^9/5 * ⁵√2 * √8 = 2^(9/5+1/5) * √2³ = 2^10/5 * 2^3/2 = 2² * 2^3/2 = 2^(2+3/2) = 2^(3 1/2)
f)
4^-7,5 : 4^-2,5 + 2^-10 = 4^-5 + 2^-10 = (2²)^-5 + 2^-10 = 2^-10 + 2^-10 =
= 2 * 2^-10 = 2^-9
Szczegółowe wyjaśnienie:
