Solve the following equation with a rational exponent: 5x43=80

Question

.(1 point)
Responses

12
12

40.32
40.32

16
16

8

Answer 1

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

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

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

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

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

So, \(x = 8\).

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