Solve by Factoring x^(2/3)-1/4=0

Rewrite ${\displaystyle x^{\frac{2}{3}}}$ as ${\displaystyle {\left(x^{\frac{1}{3}}\right)}^2}$.

Rewrite ${\displaystyle \frac{1}{4}}$ as ${\displaystyle {\left(\frac{1}{2}\right)}^2}$.

Since both terms are perfect squares, factor using the difference of squares formula, ${\displaystyle a^2-b^2=(a+b)(a-b)}$ where ${\displaystyle a=x^{\frac{1}{3}}}$ and ${\displaystyle b=\frac{1}{2}}$.

To write ${\displaystyle x^{\frac{1}{3}}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{2}{2}}$.

Combine ${\displaystyle x^{\frac{1}{3}}}$ and ${\displaystyle \frac{2}{2}}$.

Combine the numerators over the common denominator.

Move ${\displaystyle 2}$ to the left of ${\displaystyle x^{\frac{1}{3}}}$.

To write ${\displaystyle x^{\frac{1}{3}}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{2}{2}}$.

Combine ${\displaystyle x^{\frac{1}{3}}}$ and ${\displaystyle \frac{2}{2}}$.

Combine the numerators over the common denominator.

Move ${\displaystyle 2}$ to the left of ${\displaystyle x^{\frac{1}{3}}}$.

If any individual factor on the left side of the equation is equal to ${\displaystyle 0}$, the entire expression will be equal to ${\displaystyle 0}$.