Szczegółowe wyjaśnienie:
Zadanie dotyczy twierdzenia:
[tex]\left(a^n\right)^m=a^{n\cdot m}[/tex]
2.
[tex].\qquad=9^{5\cdot6}=9^{30}\\\\\left(9^5\right)^6=9^{5\cdot6}=9^{6\cdot5}=\left(9^6\right)^5\\\\.\qquad=9^{5\cdot6}=9^{30}=\left(3^2\right)^{30}=3^{2\cdot30}=3^{60}[/tex]
[tex].\qquad=\left(2^3\right)^4=2^{3\cdot4}=2^{12}\\\\8^4=8^{2\cdot2}=\left(8^2\right)^2=64^2\\\\.\qquad=\left(2^3\right)^4=2^{3\cdot4}=2^{4\cdot3}=\left(2^4\right)^3[/tex]
[tex].\qquad=\left(0,5^2\right)^{12}=0,5^{2\cdot12}=0,5^{24}\\\\0,25^{12}=0,25^{3\cdot4}=\left(0,25^3\right)^4\\\\.\qquad=0,25^{2\cdot6}=\left(0,25^2\right)^6=0,0625^6[/tex]
3.
a)
[tex]7^4=7^{2\cdot2}=\left(7^2\right)^2=49^2\\\\6^6=6^{2\cdot3}=\left(6^2\right)^3=36^3\\\\8^8=8^{2\cdot4}=\left(8^2\right)^4=64^4[/tex]
b)
[tex]3^9=3^{3\cdot3}=\left(3^3\right)^3=27^3\\\\5^6=5^{2\cdot3}=\left(5^2\right)^3=25^3\\\\5^6=5^{3\cdot2}=\left(5^3\right)^2=125^2[/tex]
c)
[tex]6^8=6^{2\cdot4}=\left(6^2\right)^4=36^4\\\\2^{20}=2^{4\cdot5}=\left(2^4\right)^5=16^5\\\\0,1^6=0,1^{3\cdot2}=\left(0,1^3\right)^2=0,001^2[/tex]
