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

To solve the equation \( 5x^{4/3} = 80 \), we can follow these steps:

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

2. To eliminate the rational exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):
\[
x = 16^{3/4}
\]

3. Calculate \( 16^{3/4} \):
- First, find \( 16^{1/4} \):
\[
16^{1/4} = 2 \quad (\text{since } 2^4 = 16)
\]

- Next, raise \( 2 \) to the power of 3:
\[
2^3 = 8
\]

4. Therefore,
\[
x = 8
\]

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

**8**