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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**