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

2. **Remove the rational exponent by raising both sides to the reciprocal of \(\frac{4}{3}\), which is \(\frac{3}{4}\)**:
\[
x = 16^{\frac{3}{4}}
\]

3. **Calculate \( 16^{\frac{3}{4}} \)**:
First, calculate \( 16^{\frac{1}{4}} \):
\[
16^{\frac{1}{4}} = 2
\]
(because \( 2^4 = 16 \))

Now raise this result to the power of 3:
\[
x = 2^3 = 8
\]

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

\[
\boxed{8}
\]