Solve the following equation with a rational exponent: 5x4/3=80.(1 point)

Question

Responses

40.32
40.32

12
12

8
8

16
16

Answer 1

To solve the equation \( 5x^{4/3} = 80 \), follow these steps:

1. First, divide both sides by 5: \[ x^{4/3} = \frac{80}{5} \] \[ x^{4/3} = 16 \]

2. Next, to eliminate the fractional exponent, raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \): \[ x = 16^{3/4} \]

3. Rewrite \( 16 \) as \( 2^4 \): \[ x = (2^4)^{3/4} \]

4. Simplify the right side: \[ x = 2^{4 \cdot \frac{3}{4}} = 2^3 = 8 \]

Thus, the solution to the equation \( 5x^{4/3} = 80 \) is: \[ \boxed{8} \]