Olá, Pedro.
[tex](x^3 + \frac1{x^2})^5=(\frac{x^5+1}{x^2})^5=\frac{(x^5+1)^5}{x^{10}}=[/tex]
[tex]=\frac{[(x^5+1)^2]^2(x^5+1)}{x^10}=\frac{(x^{10}+2x^5+1)^2(x^5+1)}{x^{10}}=[/tex]
[tex]=\frac{[(x^{10}+2x^5)^2+2(x^{10}+2x^5)+1](x^5+1)}{x^{10}}=[/tex]
[tex]=\frac{(x^{20}+4x^{15}+4x^{10}+2x^{10}+4x^5+1)(x^5+1)}{x^{10}}=\frac{(x^{20}+4x^{15}+6x^{10}+4x^5+1)(x^5+1)}{x^{10}}=[/tex]
[tex]=\frac{x^{25}+x^{20}+4x^{20}+4x^{15}+6x^{15}+6x^{10}+4x^{10}+4x^{5}+x^5+1}{x^{10}}=[/tex]
[tex]=\frac{x^{25}+5x^{20}+10x^{15}+10x^{10}+5x^5+1}{x^{10}}=[/tex]
[tex]=x^{15}+5x^{10}+10x^{5}+10+\frac{5}{x^5}+\frac{1}{x^{10}}[/tex]
