Solve the following equation with a rational exponent: 5x 4/3=80 .(1 point)

To solve the equation \( 5x^{4/3} = 80 \), we can start by isolating \( x^{4/3} \).

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

2. Next, to solve for \( x \), we can raise both sides to the power of \( \frac{3}{4} \) to undo the exponent:
\[
x = 16^{\frac{3}{4}}
\]

3. We can simplify \( 16^{\frac{3}{4}} \):
\[
16 = 2^4 \quad \text{so} \quad 16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8
\]

Therefore, the solution to the equation \( 5x^{4/3} = 80 \) is \( x = 8 \).

The correct response is **8**.