Question

Which fractions are equivalent to ?Select all that apply. 64 64 yi 764 8 1 4

Answer 1

We are given the following radical expression

`\sqrt[3]{(1)/(64)}`

Let us simplify it using the properties of radicals.

The quotient property of radicals is given by

`\sqrt[n]{(x)/(y)}=\frac{\sqrt[n]{x}}{\sqrt[n]{y}}`

Let us apply the above property

`\sqrt[3]{(1)/(64)}=\frac{\sqrt[3]{1}}{\sqrt[3]{64}}`

Further simplifying the radical

`\frac{\sqrt[3]{1}}{\sqrt[3]{64}}=\frac{1^{(1)/(3)}}{64^{(1)/(3)}}=(1)/(4)`

The cube root of 1 is 1 and the cube root of 64 is 4

Therefore, the correct options are

`\begin{gathered} \frac{\sqrt[3]{1}}{\sqrt[3]{64}} \\ (1)/(4) \end{gathered}`