To solve the equation \( x^{5/4} = 243 \), we can first rewrite \( 243 \) as a power of \( 3 \):
\[ 243 = 3^5 \]
Thus, we can rewrite the equation as:
\[ x^{5/4} = 3^5 \]
Next, we can raise both sides to the power of \( \frac{4}{5} \) to solve for \( x \):
\[ x = (3^5)^{4/5} \]
According to the laws of exponents, we can multiply the exponents:
\[ x = 3^{5 \cdot \frac{4}{5}} = 3^4 \]
Calculating \( 3^4 \):
\[ 3^4 = 81 \]
Therefore, the solution to the equation \( x^{5/4} = 243 \) is:
\[ \boxed{81} \]