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:
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First calculate \( 16^{\frac{1}{4}} \), which is the fourth root of 16: \[ 16^{\frac{1}{4}} = 2 \]
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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:
\[ \boxed{8} \]
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