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

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

1. Divide both sides by 5:
\[
x^{4/3} = \frac{80}{5} = 16
\]

2. Next, to solve for \( x \), raise 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, find \( 16^{\frac{1}{4}} \):
\[
16^{\frac{1}{4}} = 2
\]

- Now, raise this result to the power of 3:
\[
16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8
\]

Thus, the solution is \( x = 8 \).

The correct answer is: **8**.