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To solve the equation \( 5x^{4/3} = 80 \), we first isolate \( x^{4/3} \):
\[
x^{4/3} = \frac{80}{5}
\]
This simplifies to:
\[
x^{4/3} = 16
\]
Next, to solve for \( x \), we raise both sides to the power of \( \frac{3}{4} \):
\[
x = 16^{\frac{3}{4}}
\]
We can compute \( 16^{\frac{3}{4}} \) as follows:
1. First calculate \( 16^{\frac{1}{4}} \), which is the fourth root of 16:
\[
16^{\frac{1}{4}} = 2
\]
2. Next, compute \( 16^{\frac{3}{4}} \):
\[
16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8
\]
Thus, the solution to the equation \( 5x^{4/3} = 80 \) is:
\[
\boxed{8}
\]