Es seien a , b {\displaystyle {}a,b} positive reelle Zahlen und m , n ∈ N + {\displaystyle {}m,n\in \mathbb {N} _{+}} . Dann gelten die folgenden Aussagen.
![{\displaystyle {}{\sqrt[{m}]{\sqrt[{n}]{b}}}={\sqrt[{mn}]{b}}\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0c7273d8b19f983fa7f6888fd086136c520965dc)
![{\displaystyle {}{\sqrt[{m}]{ab}}={\sqrt[{m}]{a}}{\sqrt[{m}]{b}}\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ccaf606ac591b11f17ea91d37494db985a2d100f)
![{\displaystyle {}{\sqrt[{m}]{b^{-1}}}={\left({\sqrt[{m}]{b}}\right)}^{-1}\,.}](https://wikimedia.org/api/rest_v1/media/math/render/svg/578e893926ff3df9980c61ac724115256f33a183)