Solve the following equation with a rational exponent: 5x4/3=80

Question

.(1 point)
Responses

16
16

8
8

40.32
40.32

12

Answer 1

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

1. Isolate the term with the exponent: \[ x^{4/3} = \frac{80}{5} \] \[ x^{4/3} = 16 \]

2. Remove the rational exponent by raising both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \): \[ x = 16^{\frac{3}{4}} \]

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

   • First, find \( 16^{\frac{1}{4}} \): \[ 16^{\frac{1}{4}} = 2 \]
   • Then raise it to the power of 3: \[ 16^{\frac{3}{4}} = (16^{\frac{1}{4}})^3 = 2^3 = 8 \]

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