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

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

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

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

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

Now, we first calculate \( 16^{3/4} \):

1. Calculate \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad (\text{since } 16 = 2^4)
\]

2. Now raise the result to the power of 3:
\[
16^{3/4} = (16^{1/4})^3 = 2^3 = 8
\]

Thus, the solution to the equation is:

\[
\boxed{8}
\]