Odpowiedź:
[tex]a)\ \ 3^4\cdot9^2=3^4\cdot(3^2)^2=3^4\cdot3^4=3^{4+4}=3^8\\\\\\b)\ \ 4^5\cdot8^3=(2^2)^5\cdot(2^3)^3=2^{10}\cdot2^9=2^{10+9}=2^1^9\\\\\\c)\ \ 8^3:2^5=(2^3)^3:2^5=2^9:2^5=2^{9-5}=2^4\\\\\\d)\ \ 125^7:25^{10}=(5^3)^7:(5^2)^{10}=5^{21}:5^{20}=5^{21-20}=5^1\\\\\\e)\ \ (\frac{1}{9})^4:(\frac{1}{3})^3=((\frac{1}{3})^2)^4:(\frac{1}{3})^3=(\frac{1}{3})^8:(\frac{1}{3})^3=(\frac{1}{3})^{8-3}=(\frac{1}{3})^5[/tex]
[tex]f)\ \ 0,5^9:(\frac{1}{4})^4=(\frac{1}{2})^9:((\frac{1}{2})^2)^4=(\frac{1}{2})^9:(\frac{1}{2})^{8}=(\frac{1}{2})^{9-8}=(\frac{1}{2})^{1}\\\\\\g)\ \ 0,1^9:0,001^2=0,1^9:((0,1)^3)^2=0,1^9:0,1^6=0,1^{9-6}=0,1^3\\\\\\h)\ \ \dfrac{5^8}{32}\cdot\dfrac{2^1^0}{125}=\dfrac{5^8}{2^5}\cdot\dfrac{2^1^0}{5^3}=5^{8-3}\cdot2^{10-5}=5^5\cdot2^5=(5\cdot2)^5=10^5[/tex]
