Question

Scrieţi numărul x sub formă de un radical:

Answer 1

Explicație pas cu pas:

$x = \frac{ \sqrt{a \cdot \sqrt[3]{ {a}^{2} } } }{ \sqrt[12]{ {a}^{11} } } = \frac{\Big(a \cdot {a}^{ \frac{2}{3} } \Big)^{ \frac{1}{2} } }{ {a}^{\frac{11}{12}} } = \frac{\Big({a}^{1 + \frac{2}{3} } \Big)^{ \frac{1}{2} } }{ {a}^{\frac{11}{12}} } = \\ = \frac{\Big({a}^{\frac{5}{3} } \Big)^{ \frac{1}{2} } }{ {a}^{\frac{11}{12}} } = \frac{{a}^{\frac{5}{3} \cdot \frac{1}{2} }}{ {a}^{\frac{11}{12}} } = {a}^{ \frac{5}{6} - \frac{11}{12} } = {a}^{\frac{10 - 11}{12} } = {a}^{\frac{ - 1}{12} } \\ = \frac{1}{{a}^{\frac{1}{12} }} = \bf \frac{1}{ \sqrt[12]{a} } = \bf \sqrt[12]{\frac{1}{ a} }$