(3x)^(1/3)(2x)^(1/3)(16x^2)^(1/3)

 Esercizio

$\sqrt[3]{3x}\cdot\sqrt[3]{2x}\cdot\sqrt[3]{16x^2}$

 

Applicare la formula: $\left(ab\right)^n$$=a^nb^n$

$\sqrt[3]{3}\sqrt[3]{2}\sqrt[3]{16}\sqrt[3]{x}\cdot \sqrt[3]{x}\sqrt[3]{x^{2}}$

 

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

$\sqrt[3]{3}\sqrt[3]{2}\sqrt[3]{16}x^{\left(\frac{1}{3}+\frac{1}{3}\right)}\sqrt[3]{x^{2}}$

 

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

$\sqrt[3]{3}\sqrt[3]{2}\sqrt[3]{16}x^{\left(\frac{1}{3}+\frac{1}{3}+\frac{2}{3}\right)}$

 

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

$\sqrt[3]{3}\sqrt[3]{2}\sqrt[3]{16}x^{\left(\frac{2}{3}+\frac{2}{3}\right)}$

 

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

$\sqrt[3]{3}\sqrt[3]{2}\sqrt[3]{16}\sqrt[3]{x^{4}}$

$\sqrt[3]{3}\sqrt[3]{2}\sqrt[3]{16}\sqrt[3]{x^{4}}$

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