Odpowiedź:
zad.4
a)
(125 * 15)/(3³ * 5^4) = (5³ * 3 * 5)/(3³ * 5^4) = ( 5^4 * 3^-2)/5^4 = 3^-2
b)
[(3^5)^4 * 6^4)]/(9^7 * 4²) = (3^20 * 2^4 * 3^4)/[(3²)^20 * (2²)²] =
= (3^24 * 2^4)/(3^40 * 2^4) = 3^-16
c)
(9³ * 4^4)/6^10 = [(3²)³ * (2²)^4]/(2^10 * 3^10) = (3^6 * 2^8)/(2^10 * 3^10) =
= 3^-4 * 2^-2
d)
(0,25³ : 0,5³)/5³ = [(0,25 : 0,5)/5]³ = (0,5/5)³ = 0,1³ = 0,001
e)
[(8^5 * 4³)² * 25²]/(10^4 * 2^10) = [(2³)^5 * (2²)³ * 5²]²/(5^4 * 2^4 * 2^10) =
= (2^15 * 2^6 * 5²)² : (5^4 * 2^14) = (2^21 * 5²)² : (5^4 * 2^14) =
= (2^42 * 5^4)/(5^4 * 2^14) = 2^28
f)
(64² * 36^4)/(6³ * 2^6) = [(2^6)² * (6²)^4)/(2³ * 3³ * 2^6) =
= (2^12 * 2^8 * 3^8)/(2³ * 3³ * 2^6) = (2^20 * 3^8)/2^9 * 3³) = 2^11 * 3^5
zad.5
a)
(3^7 + 3^5)/10 = (3^5 * 3² + 3^5)/10 = 3^5(3² + 1)/10 = 3^4(9 + 1)/10 = 3^4 * 10/10 = 3^4
b)
3^12/(2^11 + 2^12) = 3^12/(2^10 * 2 + 2^10 * 2²) = 3^12/[2^10(2 + 2²) =
= 3^12/[2^10(2 + 4) = 3^12/(6 * 2^12) = 3^12/(3 * 2 * 2^12) = 3^11/2^13
c)
6^14/(3^15 - 3^13) = (2 * 3)^14/[3^13(3² - 1) = (2^14 * 3)/(9 - 1) = 3 * 2^14/8 =
= 3 * 2^14/2³ = 3 * 2^11
Szczegółowe wyjaśnienie: