We are given the following radical expression
[tex]\sqrt[3]{\frac{1}{64}}[/tex]
Let us simplify it using the properties of radicals.
The quotient property of radicals is given by
[tex]\sqrt[n]{\frac{x}{y}}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}[/tex]
Let us apply the above property
[tex]\sqrt[3]{\frac{1}{64}}=\frac{\sqrt[3]{1}}{\sqrt[3]{64}}[/tex]
Further simplifying the radical
[tex]\frac{\sqrt[3]{1}}{\sqrt[3]{64}}=\frac{1^{\frac{1}{3}}}{64^{\frac{1}{3}}}=\frac{1}{4}[/tex]
The cube root of 1 is 1 and the cube root of 64 is 4
Therefore, the correct options are
[tex]\begin{gathered} \frac{\sqrt[3]{1}}{\sqrt[3]{64}} \\ \frac{1}{4} \end{gathered}[/tex]
