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

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

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

This simplifies to:

\[
x^{4/3} = 16
\]

Next, to solve for \( x \), we raise both sides to the power of \( \frac{3}{4} \):

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

We can compute \( 16^{\frac{3}{4}} \) as follows:

1. First calculate \( 16^{\frac{1}{4}} \), which is the fourth root of 16:
\[
16^{\frac{1}{4}} = 2
\]

2. Next, compute \( 16^{\frac{3}{4}} \):
\[
16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8
\]

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

\[
\boxed{8}
\]