Solve the following equation with a rational exponent: 5x 4/3=80.(1 point)

To solve the equation \( 5x^{4/3} = 80 \), we first isolate \( x^{4/3} \) by dividing both sides by 5:

\[
x^{4/3} = \frac{80}{5} = 16.
\]

Next, to eliminate the rational exponent \( \frac{4}{3} \), we raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):

\[
x = 16^{\frac{3}{4}}.
\]

Now, we can simplify \( 16^{\frac{3}{4}} \):

1. First, find \( 16^{\frac{1}{4}} \):
\[
16^{\frac{1}{4}} = 2 \quad \text{(since \( 16 = 2^4 \))}.
\]

2. Then raise this result to the 3rd power:
\[
16^{\frac{3}{4}} = (2)^{3} = 8.
\]

Therefore, the solution is:

\[
\boxed{8}.
\]