(x^3+1/(x^2))^4

 Esercizio

$\left(x^3+\frac{1}{x^2}\right)^4$

 

Applicare la formula: $\left(a+b\right)^4$$=a^4+4a^3b+6a^2b^2+4ab^3+b^4$, dove $a=x^3$, $b=\frac{1}{x^2}$ e $a+b=x^3+\frac{1}{x^2}$

$x^{12}+\frac{4x^{9}}{x^2}+6x^{6}\left(\frac{1}{x^2}\right)^2+4x^3\left(\frac{1}{x^2}\right)^3+\left(\frac{1}{x^2}\right)^4$

 

Applicare la formula: $\frac{a^m}{a^n}$$=a^{\left(m-n\right)}$, dove $a^n=x^2$, $a^m=x^{9}$, $a=x$, $a^m/a^n=\frac{4x^{9}}{x^2}$, $m=9$ e $n=2$

$x^{12}+4x^{7}+6x^{6}\left(\frac{1}{x^2}\right)^2+4x^3\left(\frac{1}{x^2}\right)^3+\left(\frac{1}{x^2}\right)^4$

 

Applicare la formula: $\left(\frac{a}{b}\right)^n$$=\frac{a^n}{b^n}$, dove $a=1$, $b=x^2$ e $n=2$

$x^{12}+4x^{7}+6x^{6}\left(\frac{1}{x^{4}}\right)+4x^3\left(\frac{1}{x^2}\right)^3+\left(\frac{1}{x^2}\right)^4$

 

Applicare la formula: $\left(\frac{a}{b}\right)^n$$=\frac{a^n}{b^n}$, dove $a=1$, $b=x^2$ e $n=3$

$x^{12}+4x^{7}+6x^{6}\left(\frac{1}{x^{4}}\right)+4x^3\left(\frac{1}{x^{6}}\right)+\left(\frac{1}{x^2}\right)^4$

 

Applicare la formula: $\left(\frac{a}{b}\right)^n$$=\frac{a^n}{b^n}$, dove $a=1$, $b=x^2$ e $n=4$

$x^{12}+4x^{7}+6x^{6}\left(\frac{1}{x^{4}}\right)+4x^3\left(\frac{1}{x^{6}}\right)+\frac{1}{x^{8}}$

$x^{12}+4x^{7}+6x^{6}\left(\frac{1}{x^{4}}\right)+4x^3\left(\frac{1}{x^{6}}\right)+\frac{1}{x^{8}}$

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