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

 Esercizio

$\left(\sqrt{x}+\frac{1}{x^3}\right)^n$

 

Applicare la formula: $a+\frac{b}{c}$$=\frac{b+ac}{c}$, dove $a=\sqrt{x}$, $b=1$, $c=x^3$, $a+b/c=\sqrt{x}+\frac{1}{x^3}$ e $b/c=\frac{1}{x^3}$

$\left(\frac{1+\sqrt{x}x^3}{x^3}\right)^n$

 

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

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

 

Applicare la formula: $\frac{a}{b}+c$$=\frac{a+cb}{b}$, dove $a/b+c=\frac{1}{2}+3$, $a=1$, $b=2$, $c=3$ e $a/b=\frac{1}{2}$

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

 

Applicare la formula: $ab$$=ab$, dove $ab=3\cdot 2$, $a=3$ e $b=2$

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

 

Applicare la formula: $a+b$$=a+b$, dove $a=1$, $b=6$ e $a+b=1+6$

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

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

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