Salutare!
a)
[tex]\bf [(-9)^{n}]^{2}=81^{3}[/tex]
[tex]\bf (-9)^{n \cdot 2}=(9^{2})^{3}[/tex]
[tex]\bf (-9)^{2n}=9^{2\cdot 3}[/tex]
[tex]\bf (-9)^{2n}=9^{6}[/tex]
[tex]\bf 9^{2n}=9^{6}\Rightarrow 2n =6\Rightarrow \boxed{\bf n = 3}[/tex]
b)
[tex]\bf (+8)^{n}\cdot(-3)^{n}=(-24)^{6}[/tex]
[tex]\bf (-24)^{n}=(-24)^{6}\Rightarrow \boxed{\bf n=6}[/tex]
c)
[tex]\bf (-8)^{n}\cdot(+18)^{n}=(-144)^{5}[/tex]
[tex]\bf (-144)^{n}=(-144)^{5} \Rightarrow \boxed{\bf n = 5}[/tex]
d)
[tex]\bf [(-12)^{2}]^{n}=144^{3}[/tex]
[tex]\bf (-12)^{n \cdot 2}=(12^{2})^{3}[/tex]
[tex]\bf (-12)^{2n}=12^{2\cdot 3}[/tex]
[tex]\bf 12^{2n}=12^{6}\Rightarrow 2n =6\Rightarrow \boxed{\bf n = 3}[/tex]
