Explicación paso a paso:
[tex]N = \sqrt[3]{a^{2} } . \sqrt[4]{a^{3} } . \sqrt{a^{5} } \\\\N = a^{\frac{2}{3} } . a^{\frac{3}{4} } . a^{\frac{5}{2} } \\\\N = a^{\frac{2}{3} + \frac{3}{4} + \frac{5}{2} }\\\\N = a^{\frac{2.4}{3.4} + \frac{3.3}{4.3} + \frac{5.6}{2.6} }\\\\N = a^{\frac{8}{12} + \frac{9}{12} + \frac{30}{12} }\\\\N = a^{\frac{8+9+30}{12} }\\\\N = a^{\frac{47}{12} }\\\\N = \sqrt[12]{a^{47} }[/tex]
