Witaj :)
a]
[tex]5^2\cdot25=5^2\cdot5^2=5^{2+2}=5^4\\[/tex]
b]
[tex]125\cdot5^6=5^3\cdot5^6=5^{3+6}=5^9\\[/tex]
c]
[tex]\frac{125^8}{5}=\frac{(5^3)^8}{5}=\frac{5^{3\cdot8}}{5}=\frac{5^{24}}{5}=5^{24-1}=5^{23}\\[/tex]
d]
[tex]5^{18}:25^6=5^{18}:(5^2)^6=5^{18}:5^{2\cdot6}=5^{18}:5^{12}=5^{18-12}=5^6\\[/tex]
e]
[tex](5^7\cdot25)^2=(5^7\cdot5^2)^2=(5^{7+2})^2=(5^9)^2=5^{9\cdot2}=5^{18}\\[/tex]
f]
[tex]25^{10}:125^5=(5^2)^{10}:(5^3)^5=5^{2\cdot10}:5^{3\cdot5}=5^{20}:5^{15}=5^{20-15}=5^5\\[/tex]
g]
[tex](125^2)^5\cdot5=125^{2\cdot5}\cdot5=125^{10}\cdot5=(5^3)^{10}\cdot5=5^{3\cdot10}\cdot5=5^{30}\cdot5=5^{30+1}=5^{31}\\[/tex]
h]
[tex](\frac{5^9}{125})^4=(\frac{5^9}{5^3})^4=(5^{9-3})^4=(5^6)^4=5^{6\cdot4}=5^{24}\\[/tex]
