Esercizio
$\sqrt[n]{\frac{9^{n+\frac{1}{4}}\sqrt{3^{n-2}}}{\sqrt{\frac{1}{3}\sqrt{3^n}}}}$
Soluzione passo-passo
Impara online a risolvere i problemi di passo dopo passo. ((9^(n+1/4)3^(n-2)^(1/2))/((1/33^n^(1/2))^(1/2)))^(1/n). Simplify \sqrt{3^n} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals n and n equals \frac{1}{2}. Simplify \sqrt{3^{\left(n-2\right)}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals n-2 and n equals \frac{1}{2}. Applicare la formula: \left(ab\right)^n=a^nb^n. Applicare la formula: \frac{a^m}{a^n}=a^{\left(m-n\right)}, dove a^n=3^{\frac{1}{4}n}, a^m=3^{\frac{1}{2}\left(n-2\right)}, a=3, a^m/a^n=\frac{9^{\left(n+\frac{1}{4}\right)}3^{\frac{1}{2}\left(n-2\right)}}{\frac{1}{\sqrt{3}}3^{\frac{1}{4}n}}, m=\frac{1}{2}\left(n-2\right) e n=\frac{1}{4}n.
((9^(n+1/4)3^(n-2)^(1/2))/((1/33^n^(1/2))^(1/2)))^(1/n)
Risposta finale al problema
$\left(9^{\left(n+\frac{1}{4}\right)}3^{\left(\frac{1}{2}n-\frac{1}{2}-\frac{1}{4}n\right)}\right)^{\frac{1}{n}}$