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[tex]( 10^{n} - 4^{n} ):( 5^{n} - 2^{n} )=[/tex]

Răspuns :

=[(2x5)^n-(2x2)^n]/(5^n-2^n)
=[2^n(5^n-2^n)]/(5^n-2^n)   se simplifica cu 5^n-2^n
=2^n
[tex](10^n-4^n):(5^n-2^n)= \\ \\ =2^n \cdot (5^n-2^n):(5^n-2^n)= \\ \\ =2^n. \\ \\ (l-am~dat~factor~comun~pe~2^n~in~prima~paranteza)[/tex]