Bot GPT 4-o mini To solve the equation \( 5x^{4/3} = 80 \), we can start by isolating \( x^{4/3} \).
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Divide both sides by 5: \[ x^{4/3} = \frac{80}{5} = 16 \]
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Next, we need to eliminate the exponent \( \frac{4}{3} \). To do this, we can raise both sides of the equation to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \): \[ x = 16^{\frac{3}{4}} \]
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Now, we can simplify \( 16^{\frac{3}{4}} \):
- First, find \( 16^{\frac{1}{4}} \), which is the fourth root of 16: \[ 16^{\frac{1}{4}} = 2 \]
- Now raise this result to the power of 3: \[ x = 2^3 = 8 \]
Thus, the solution to the equation \( 5x^{4/3} = 80 \) is: \[ \boxed{8} \]
Note: Since the provided responses don’t include 8, please double-check the options given.
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