Szczegółowe wyjaśnienie:
Zadanie 6
[tex](5^{9}:5^{3})^{2}=(5^{9-3})^{2}=(5^{6})^{2}=5^{6*2}=5^{12}[/tex]
[tex](\frac{5^{9}}{5^{4}} )^{2}=(5^{9-4})^2=(5^5)^2=5^{5*2}=5^{10}[/tex]
[tex](5^4)^5:5^8=5^{4*5}:5^8=5^{20-8}=5^{12}[/tex]
[tex]\frac{5^{14}}{(5^2)^4}=\frac{5^{14}}{5^{2*4}}=5^{14-8}=5^6[/tex]
[tex]\frac{(5^4)^3}{5^9:5^3} =\frac{5^{4*3}}{5^{9-3}}=5^{12-6}=5^6[/tex]
[tex](\frac{5^5:5^2}{5} )^5=(\frac{5^{5-2}}{5^1})^5 =(5^{3-1})^5=5^{2*5}=5^{10}[/tex]
Zadanie 7
[tex]\frac{(2^2)^4*2^3}{2^5} =\frac{2^{8+3}}{2^5} =2^{11-5}=2^6[/tex]
[tex]\frac{(4^4)^3}{(4*4^2)^3} =\frac{4^{4*3}}{(4^{1+2})^3} =\frac{4^{12}}{4^{3*3}}=4^{12-9}=4^3=(2^2)^3 =2^{2*3}= 2^6[/tex]
[tex](\frac{8^5:8^3}{8} )^2=(\frac{8^{5-3}}{8^1} )^2=(8^{2-1})^2=8^2=(2^3)^2=2^{3*2}=2^6[/tex]
Ramka:
[tex]a^n*a^m=a^{n+m}\\a^n:a^m=\frac{a^n}{a^m} =a^{n-m}\\(a^n)^m=a^{n*m}[/tex]
