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

Question

Responses

40.32
40.32

8
8

16
16

12
12

Answer 1

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

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

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, calculate \( 16^{\frac{1}{4}} \): \[ 16^{\frac{1}{4}} = 2 \] (because \( 2^4 = 16 \))

   Now raise this result to the power of 3: \[ x = 2^3 = 8 \]

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

\[ \boxed{8} \]