Odpowiedź:
1.
a)
7^9 * 7^6 = 7^15
b)
5^9 * 5 * 5^7 =5^10 * 5^7 = 5^17
c)
(1 1/7)^9 : (1 1/7)^4 = (1 1/7)^5
2.
a)
16 * 2^5 * 2^6 = 2^4 * 2^11 = 2^15
b)
81 * 3³ : 3^5 = 3^4 * 3^-2 = 3²
c)
64 * 8 : 2^7 = 2^6 * 2³ : 2^7 = 2^9 : 2^7 = 2²
3.
a)
(6³)^6 =6^18
b)
(-5^5)^5 = (-5)^25
c)
[(-0,1)^6]³ = (-0,1)^18
d)
[(2²)³]^4 = (2^6)^4 = 2^24
4.
a)
4^7 = (2²)^7 = 2^14
b)
32^10 = (2^5)^10 = 2^50
c)
(8³)^4 = [(2³)³]^4 = (2^9)^4 = 2^36
d)
(16^5)^4 = [(2^4)^5]^4 = (2^20)^4 = 2^80
5.
(3^4)^5 = 3^20, 27^6 = (3³)^6 = 3^18, (3²)^5 = 3^10, (3^5)² = 3^10
(3²)^5 = (3^5)² < 27^6 < (3^5)² < (3^4)^5
6.
a)
(3x)^4 = 16x^4
b)
(-8x³)² = 64x^6
c)
(-x^4y^6)³ = -x^12y^18
d)
(-5x^5/2y)³ = -x^15/8y³
7.
a)
100^4 : 50^4 = (100/50)^4 = 2^4 = 16
b)
(5 1/2)^10 * (2/11)^10 = (5 1/2 * 2/11)^10 = (11/2 * 2/11)^10 = 1^10 = 1
c)
(-0,9)³ : 9³ = (-0,9 : 9)³ = (-0,1)³ = -0,001
d)
(-5/13)³ : (1/13)³ = (-5/13 * 13)³ = (-5)³ = -125
Szczegółowe wyjaśnienie:
