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Bot GPT 4-o mini To solve the equation \( 5x^{4/3} = 80 \), we first isolate the term with the exponent:
\[
x^{4/3} = \frac{80}{5}
\]
\[
x^{4/3} = 16
\]
Next, we raise both sides to the reciprocal of the exponent, which is \( \frac{3}{4} \):
\[
\left(x^{4/3}\right)^{3/4} = 16^{3/4}
\]
\[
x = 16^{3/4}
\]
Now, we simplify \( 16^{3/4} \). We can break it down as follows:
\[
16 = 2^4
\]
So:
\[
16^{3/4} = (2^4)^{3/4} = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8
\]
Thus, the solution to the equation is:
\[
\boxed{8}
\]
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