Zadanie 8 Oblicz. a) (3\frac{1}{4})^6*(\frac{4}{13})^6
b) (5,25)^7*(\frac{8}{3})^7*(\frac{1}{7})^7
c) (1\frac{1}{4})^4:(\frac{1}{4})^4
Zadanie 9 Oblicz. a) \frac{10^4*9^2}{6^4}
b) \frac{3^4*49^2}{14^4:2^4}
c) \frac{2^5*(-6)^5}{4^5}
źródło:
Zadanie 8 a) (3\frac{1}{4})^6*(\frac{4}{13})^6=(\frac{\not13^1}{\not4^1}*\frac{\not4^1}{\not13^1})^6=1^6=1 b) (5,25)^7*(\frac{8}{3})^7*(\frac{1}{7})^7=(5,25*\frac{8}{3}*\frac{1}{7})^7=(\frac{42}{21})^7=2^7=128 c) (1\frac{1}{4})^4:(\frac{1}{4})^4=(\frac{5}{4}:\frac{1}{4})^4=(\frac{5}{4}*\frac{4}{1})^4=5^4=625
Zadanie 9 a) \frac{10^4*9^2}{6^4}=\frac{10^4*(3^2)^2}{6^4}=\frac{10^4*3^4}{6^4}=\frac{(10*3)^4}{6^4}=(\frac{30}{6})^4=5^4=625 b) \frac{3^4*49^2}{14^4:2^4}=\frac{3^4*(7^2)^2}{(14:2)^4}=\frac{3^4*7^4}{7^4}=3^4=81 c) \frac{2^5*(-6)^5}{4^5}=\frac{[(2*(-6)]^5}{4^5}=(\frac{-12}{4})^5=(-3)^5=-243