To solve the equation \( 5x^{4/3} = 80 \), follow these steps:
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Isolate the term with \( x \): \[ x^{4/3} = \frac{80}{5} \] Simplifying the right side: \[ x^{4/3} = 16 \]
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Eliminate the rational exponent by raising both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \): \[ x = 16^{3/4} \]
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Calculate \( 16^{3/4} \):
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First, compute \( 16^{1/4} \): \[ 16^{1/4} = 2 \] since \( 2^4 = 16 \).
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Now, compute \( 16^{3/4} \): \[ 16^{3/4} = (16^{1/4})^3 = 2^3 = 8 \]
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Final result: Thus, the solution to the equation \( 5x^{4/3} = 80 \) is: \[ \boxed{8} \]
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