To solve the equation \( 5x^{4/3} = 80 \), we first isolate \( x^{4/3} \):
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Divide both sides by 5: \[ x^{4/3} = \frac{80}{5} = 16 \]
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Next, to solve for \( x \), raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \): \[ x = 16^{\frac{3}{4}} \]
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Calculate \( 16^{\frac{3}{4}} \):
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First, find \( 16^{\frac{1}{4}} \): \[ 16^{\frac{1}{4}} = 2 \]
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Now, raise this result to the power of 3: \[ 16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8 \]
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Thus, the solution is \( x = 8 \).
The correct answer is: 8.