Odpowiedź:
1.
a)
8³ * 8^4 = 8^7
b)
4² * 4^1 * 4^9 = 4³ * 4^9 = 4^12
c)
12^5 : 12² = 12^7
d)
(6^5)³ = 6^15
2.
5³ * 20³ = (5 * 20)³ = 100³ = 100 00 00
(3/4)^5 * (1 1/3)^5 = (3/4 * 4/3)^5 = 1^5 = 1
0,7² * (-10)² = [0,7 * (-10)]² = (-7)² = 49
12^4 : 4^4 = (12 : 4)^4 = 3^4 = 81
e)
8^5 : (-8)^5 = (-1)^5 = -1
3.
(9³)² : 3^4 = [(3²)³]² : 3^4 = (3^6)² : 3^4 = 3^12 : 3^4 = 3^8
125^7 : 25³ = (5³)^7 : (5²)³ = 5^21 : 5^6 = 5^15
4^10 + 4^10 + 4^10 + 4^10 = 4 * 4^10 = 4^11
Szczegółowe wyjaśnienie:
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Odpowiedź:
1.
a)
8³ * 8^4 = 8^7
b)
4² * 4^1 * 4^9 = 4³ * 4^9 = 4^12
c)
12^5 : 12² = 12^7
d)
(6^5)³ = 6^15
2.
a)
5³ * 20³ = (5 * 20)³ = 100³ = 100 00 00
b)
(3/4)^5 * (1 1/3)^5 = (3/4 * 4/3)^5 = 1^5 = 1
c)
0,7² * (-10)² = [0,7 * (-10)]² = (-7)² = 49
d)
12^4 : 4^4 = (12 : 4)^4 = 3^4 = 81
e)
8^5 : (-8)^5 = (-1)^5 = -1
3.
a)
(9³)² : 3^4 = [(3²)³]² : 3^4 = (3^6)² : 3^4 = 3^12 : 3^4 = 3^8
b)
125^7 : 25³ = (5³)^7 : (5²)³ = 5^21 : 5^6 = 5^15
c)
4^10 + 4^10 + 4^10 + 4^10 = 4 * 4^10 = 4^11
d)
(9³)² : 3^4 = [(3²)³]² : 3^4 = (3^6)² : 3^4 = 3^12 : 3^4 = 3^8
Szczegółowe wyjaśnienie: