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

Question

Responses

12
12

8
8

16
16

40.32

Answer 1

To solve the equation 5x^(4/3) = 80, we need to isolate the variable x.

First, we can divide both sides of the equation by 5 to get:
x^(4/3) = 16

Next, we can raise both sides of the equation to the power of 3/4 to eliminate the rational exponent:
(x^(4/3))^(3/4) = 16^(3/4)

This simplifies to:
x = 16^(3/4)

To evaluate 16^(3/4), we can simplify it as follows:
16^(3/4) = (2^4)^(3/4) = 2^(4 * (3/4)) = 2^3 = 8

Therefore, the value of x is 8.