Quando o índice do radical é negativo, aplicamos a propriedade que relaciona o radical com o expoente:
Assim, se o índice for negativo, temos:
Exemplos:
Assim, podemos concluir que:
Lembrar
![\[ \boxed{\sqrt[n]{a} = a^{\tfrac{1}{-n}}} \]](https://cod3x.net/edulab/wp-content/ql-cache/quicklatex.com-8bf72343ba3f749d62b3122b9cde9efb_l3.svg "Rendered by QuickLaTeX.com")
![\[ \boxed{\sqrt[-n]{a} = a^{\tfrac{1}{-n}} = a^{-\tfrac{1}{n}} = \frac{1}{a^{\tfrac{1}{n}}} = \frac{1}{\sqrt[n]{a}}} \]](https://cod3x.net/edulab/wp-content/ql-cache/quicklatex.com-2b8d48eed2671a9c5398a6194d599c00_l3.svg "Rendered by QuickLaTeX.com")
![\[ \begin{aligned} (a)\;& \sqrt[-2]{9} = \frac{1}{\sqrt[2]{9}} = \frac{1}{3}, \\[6pt] (b)\;& \sqrt[-3]{8} = \frac{1}{\sqrt[3]{8}} = \frac{1}{2}, \\[6pt] (c)\;& \sqrt[-4]{16} = \frac{1}{\sqrt[4]{16}} = \frac{1}{2}, \\[6pt] (d)\;& \sqrt[-2]{25} = \frac{1}{\sqrt[2]{25}} = \frac{1}{5}. \end{aligned} \]](https://cod3x.net/edulab/wp-content/ql-cache/quicklatex.com-5c1f4d09cd134d5307c5d6f8c633f95d_l3.svg "Rendered by QuickLaTeX.com")
![\[ \boxed{\sqrt[-n]{a} = \frac{1}{\sqrt[n]{a}}} \]](https://cod3x.net/edulab/wp-content/ql-cache/quicklatex.com-cb4c8924bbcfd7b3e29ffa4ad91fe211_l3.svg "Rendered by QuickLaTeX.com")