Esercizio
$\sqrt[3]{\sqrt{x\sqrt{x\sqrt{x}^m}=x^5}}$
Soluzione passo-passo
Impara online a risolvere i problemi di poteri dei poteri passo dopo passo. (x(xx^(1/2)^m)^(1/2)=x^5)^(1/2)^(1/3). Simplify \sqrt[3]{\sqrt{x\sqrt{x\left(\sqrt{x}\right)^m}=x^5}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals \frac{1}{3}. Simplify \left(\sqrt{x}\right)^m using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2} and n equals m. Applicare la formula: x\cdot x^n=x^{\left(n+1\right)}, dove x^nx=x\cdot x^{\frac{1}{2}m}, x^n=x^{\frac{1}{2}m} e n=\frac{1}{2}m. Simplify \sqrt{x^{\left(\frac{1}{2}m+1\right)}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals \frac{1}{2}m+1 and n equals \frac{1}{2}.
(x(xx^(1/2)^m)^(1/2)=x^5)^(1/2)^(1/3)
Risposta finale al problema
$\sqrt[6]{x^{\left(\frac{1}{4}m+\frac{3}{2}\right)}=x^5}$