Odpowiedź:
7.
a) 3^4 * 9^2 = 3^4 * (3^2)^2 = 3^8
b) 4^5 * 8^3 = (2^2)^5 * (2^3)^3 = 2^19
c) 8^3 / 2^5 = (2^3)^3 / 2^5 = 2^4
d) 125^7 / 25^10 = (5^3)^7 / (5^2)^10 = 5^1 (po prostu 5)
e) (1/9)^4 / (1/3)^3 = [(1/3)^2]^4 / (1/3)^3 = (1/3)^5
f) 0,5^9 / (1/4)^4 = 0,5^9 / (0,5^2)^4 = 0,5
g) 0,1^9 / 0,001^2 = 10^-9 / (10^-3)^2 = 10^-3
h) (5^8/32)*(2^10/125) = (5^8/2^5)*(2^10/5^3)= 5^5*2^5 = 10^5
8.
a) (2^10 * 2^5 *7^4)^2 = 2^m * 7^n
(2^15*7^4)^2 = 2^m * 7^n
2^30*7^8 = 2^m * 7^n
m = 30
n = 8
b) [(3^4*5^7)^3]/5^9 = 3^m * 5^n
(3^12*5^21)/5^9 = 3^m * 5^n
3^12 * 5^12 = 3^m * 5^n
m = n = 12
c) 4 * [(2^3/3^4)]^10 = 2^m/3^n
2^2 * (2^30/3^40) = 2^m/3^n
2^32/3^40 = 2^m/3^n
m = 32
n = 40
d) [(7^3/5^2)^3] * [(5^3/7^5)^4] = 5^m/7^n
(7^9/5^6) * (5^12/7^20) = 5^m/7^n
5^7/7^11 = 5^m/7^n
m = 6
n = 11
Szczegółowe wyjaśnienie:
