[tex]I.\\\\L=3^{4} -3^{0} =3\cdot 3\cdot 3\cdot 3 - 1=81-1=80\\\\P=80\\\\L=P~~\Rightarrow~~podana~~rownosc~~jest~~prawdziwa\\\\II.\\\\L=1-(-3)^{2} =1-(-3)\cdot (-3)=1-9=-8\\\\P=10\\\\L\neq P ~~\Rightarrow~~podana~~rownosc~~nie~~jest~~prawdziwa\\\\III.\\\\L=4^{5} +4^{7} =4^{5} +4^{2+5} =4^{5} +4^{2} \cdot 4^{5} =4^{5}\cdot (1+4^{2} )=4^{5} \cdot (1+16)=17\cdot 4^{5} \\\\P=4^{12} =4^{7+5} =4^{7} \cdot 4^{5} =16~384\cdot 4^{5} \\\\L\neq P ~~\Rightarrow~~podana~~rownosc~~nie~~jest~~prawdziwa[/tex]
Korzystam ze wzorów:
[tex]x^{n} \cdot x^{m} =x^{n+m} \\\\x^{0} =1,~~x\neq 0~~\Rightarrow~~x\in R - \{ 0 \}[/tex]
