Esercizio
$\sqrt{x\sqrt{x\sqrt{x}}}$
Soluzione passo-passo
Impara online a risolvere i problemi di potenza di un prodotto passo dopo passo. (x(xx^(1/2))^(1/2))^(1/2). Applicare la formula: x\cdot x^n=x^{\left(n+1\right)}, dove x^nx=x\sqrt{x}, x^n=\sqrt{x} e n=\frac{1}{2}. Simplify \sqrt{\sqrt{x^{3}}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{3}{2} and n equals \frac{1}{2}. Applicare la formula: x\cdot x^n=x^{\left(n+1\right)}, dove x^nx=x\cdot x^{\frac{3}{2}\cdot \frac{1}{2}}, x^n=x^{\frac{3}{2}\cdot \frac{1}{2}} e n=\frac{3}{2}\cdot \frac{1}{2}. Simplify \sqrt{x^{\left(\frac{3}{2}\cdot \frac{1}{2}+1\right)}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{3}{2}\cdot \frac{1}{2}+1 and n equals \frac{1}{2}.
(x(xx^(1/2))^(1/2))^(1/2)
Risposta finale al problema
$\sqrt[8]{x^{7}}$