To solve the equation \( x^3 = \frac{27}{8} \), you can take the cube root of both sides.
First, let's write the equation:
\[ x = \sqrt[3]{\frac{27}{8}} \]
Now, we can simplify \( \frac{27}{8} \):
\[ \frac{27}{8} = \frac{3^3}{2^3} \]
Consequently, the cube root can be simplified as follows:
\[ \sqrt[3]{\frac{27}{8}} = \frac{\sqrt[3]{27}}{\sqrt[3]{8}} = \frac{3}{2} \]
Therefore, the solution for \( x \) is:
\[ x = \frac{3}{2} \]