To solve the equation \( 5x^{4/3} = 80 \), we'll first isolate the \( x^{4/3} \) term.
- Divide both sides by 5:
\[ x^{4/3} = \frac{80}{5} = 16 \]
- Now we will eliminate the exponent by raising both sides to the reciprocal of the exponent \( \frac{3}{4} \):
\[ x = 16^{\frac{3}{4}} \]
-
We can simplify \( 16^{\frac{3}{4}} \):
-
First, we find \( 16^{\frac{1}{4}} \): \[ 16^{\frac{1}{4}} = 2 \] because \( 2^4 = 16 \).
-
Now raise this result to the power of 3: \[ 16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8 \]
-
So, the solution to the equation \( 5x^{4/3} = 80 \) is:
\[ \boxed{8} \]
Thus, the correct response is 8.