Solve the following equation with a rational exponent: 5x43=80.(1 point)

To solve the equation \( 5x^{4/3} = 80 \), follow these steps:

1. **Isolate \( x^{4/3} \)**:
\[
x^{4/3} = \frac{80}{5} = 16
\]

2. **Raise both sides to the power of \( \frac{3}{4} \)** to solve for \( x \):
\[
x = 16^{3/4}
\]

3. **Calculate \( 16^{3/4} \)**:
- First, find \( 16^{1/4} \). Since \( 16 = 2^4 \), we have:
\[
16^{1/4} = 2
\]
- Now raise it to the power of 3:
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]

Thus, the solution to the equation \( 5x^{4/3} = 80 \) is \( x = 8 \).

**Final answer: 8**.