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

Question

Responses

16
16

40.32
40.32

8
8

12

Answer 1

To solve the equation \( 5x^{4/3} = 80 \), we first isolate \( x^{4/3} \):

\[ x^{4/3} = \frac{80}{5} = 16 \]

Next, we raise both sides to the reciprocal of \( \frac{4}{3} \), which is \( \frac{3}{4} \):

\[ x = 16^{3/4} \]

Now, we first calculate \( 16^{3/4} \):

1. Calculate \( 16^{1/4} \): \[ 16^{1/4} = 2 \quad (\text{since } 16 = 2^4) \]

2. Now raise the result to the power of 3: \[ 16^{3/4} = (16^{1/4})^3 = 2^3 = 8 \]

Thus, the solution to the equation is:

\[ \boxed{8} \]