a) [tex]3^4 * 9^2 = 3^4 * (3^2)^2 = 3^4 * 3^4 = 3^8[/tex]
b) [tex]4^5 * 8^3 = (2^2)^5 * (2^3)^3 = 2^{10}*2^9 = 2^{19}[/tex]
c) [tex]8^3:2^5 = (2^3)^3 : 2^5 = 2^9 : 2^5 = 2^4[/tex]
d) [tex]125^7 : 25^{10} = (5^3)^7 * (5^2)^{10} = 5^{21} : 5^{20} = 5^1[/tex]
e) [tex](\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})^5[/tex]
f) [tex]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})^1[/tex]
g) [tex]0,1^9 : 0,001^2 = (\frac{1}{10})^9 : (\frac{1}{1000})^2 = (\frac{1}{10})^9 : ((\frac{1}{10})^3)^2= (\frac{1}{10})^9 : (\frac{1}{10})^6 = (\frac{1}{10})^3[/tex]
h) [tex]\frac{5^8}{32} * \frac{2^{10}}{125} = \frac{5^8}{2^5} * \frac{2^{10}}{5^3} = 5^{8-3} * 2^{10-5} = 5^5 * 2^5 = (5*2)^5 = 10^5[/tex]
