To solve the equation \( x^{5/4} = 243 \), we can first express 243 as a power of 3:
\[ 243 = 3^5 \]
Now we rewrite the equation:
\[ x^{5/4} = 3^5 \]
To solve for \( x \), we can raise both sides to the power of \( \frac{4}{5} \):
\[ x = (3^5)^{4/5} \]
Using the property of exponents \( (a^m)^n = a^{mn} \), we have:
\[ x = 3^{5 \cdot \frac{4}{5}} \] \[ x = 3^4 \] \[ x = 81 \]
Thus, the correct answer is:
81