Esercizio
$a\sqrt[6]{2^3}\cdot a\sqrt[6]{2^2}\text{\cdot}a\sqrt[6]{2}\cdot2\sqrt[6]{a^3}\cdot2\sqrt[6]{a}$
Soluzione passo-passo
Impara online a risolvere i problemi di moltiplicare potenze della stessa base passo dopo passo. Simplify the algebraic expression a2^3^(1/6)a2^2^(1/6)a*2^(1/6)*2a^3^(1/6)*2a^(1/6). Applicare la formula: ab=ab, dove ab=2\cdot 2\sqrt[6]{2^3}\sqrt[6]{2^2}\sqrt[6]{2}a\cdot a\cdot a\sqrt[6]{a^3}\sqrt[6]{a}, a=2 e b=2. Simplify \sqrt[6]{2^3} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals \frac{1}{6}. Applicare la formula: x^mx^n=x^{\left(m+n\right)}, dove x=2, m=\frac{1}{2} e n=\frac{1}{6}. Applicare la formula: x\cdot x^n=x^{\left(n+1\right)}, dove x^nx=4\sqrt[3]{\left(2\right)^{2}}\sqrt[6]{2^2}a\cdot a\cdot a\sqrt[6]{a^3}\sqrt[6]{a}, x=a, x^n=\sqrt[6]{a} e n=\frac{1}{6}.
Simplify the algebraic expression a2^3^(1/6)a2^2^(1/6)a*2^(1/6)*2a^3^(1/6)*2a^(1/6)
Risposta finale al problema
$4\sqrt[3]{\left(2\right)^{2}}\sqrt[6]{2^2}\sqrt[6]{a^{19}}\sqrt[6]{a^3}$