Solve the following equation with a rational exponent: 5x43=80.(1 point)

Question

Responses

40.32
40.32

16
16

8
8

12

Answer 1

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

1. Isolate \( x^{4/3} \): \[ x^{4/3} = \frac{80}{5} = 16 \]

2. Raise both sides to the power of \( \frac{3}{4} \) to solve for \( x \): \[ x = 16^{3/4} \]

3. Calculate \( 16^{3/4} \):

   • First, find \( 16^{1/4} \). Since \( 16 = 2^4 \), we have: \[ 16^{1/4} = 2 \]
   • Now raise it to the power of 3: \[ 16^{3/4} = (16^{1/4})^3 = 2^3 = 8 \]

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

Final answer: 8.