Equivalence relation for which there are infinitely many equivalence classes.

Question

On set $\mathbb{R}$ and the relation on it where $x\sim y$ if $x^{4}=y^{4}$. Then $\sim $ is equivalence relation for which there are infinitely many equivalence classes, one of which consists of a single element and, and the rest of two elements. How to go about evaluating equivalence classes of $\sim$

Answer 1

The quotient set is $$\mathbb{R}/\sim~~=\{\{a,-a\}|a \in \mathbb{R}\}$$

because $x \sim y$ if and only if $x=\pm y$