[tex]\it 3)\ a)n^7:n^3=(-5)^4 \Rightarrow n^{7-3}=625 \Rightarrow n^4=625 \Rightarrow (n^2)^2=25^2 \Rightarrow \\ \\ \Rightarrow n^2=25 \Rightarrow \sqrt{n^2}=\sqrt{25} \Rightarrow |n|=5 \Rightarrow n=\pm5 \Rightarrow n\in\{-5,\ 5\}\\ \\ b)\ (n^7)^3=(-5)^{21} \Rightarrow n^{21}=(-5)^{21} \Rightarrow n=-5\\ \\ c)\ (n^9)^5=[(-7)^{15}]^3 \Rightarrow n^{45}=(-7)^{45} \Rightarrow n=-7\\ \\ \\ 2)c)\ [(-12)^2]^n=144^3 \Rightarrow 144^n=144^3 \Rightarrow n=3[/tex]
[tex]\it b)\ (+8)^n\cdot(-3)^n=(-24)^6 \Rightarrow [8\cdot(-3)]^n=(-24)^6 \Rightarrow \\ \\ \Rightarrow (-24)^n=(-24)^6 \Rightarrow n=6\\ \\ \\ a)\ [(-9)^n]^2=81^3 \Rightarrow [(-9)^2]^n=81^3 \Rightarrow 81^n=81^3\Rightarrow n=3[/tex]
