Question

Solve the following equation with a rational exponent: 2x32=16 .(1 point)
Responses

8
8

no solution
no solution

84
84

4

Answer 1

To solve the equation, we need to isolate the variable x.
First, we need to get rid of the rational exponent by raising both sides of the equation to the reciprocal power. The reciprocal of 1/2 is 2/1 (or simply 2).

So we have:
(2x)^(1/2) = 16

Now we can square both sides of the equation to eliminate the rational exponent.

(2x)^(1/2)^2 = 16^2
2x = 256

Divide both sides of the equation by 2 to solve for x:
2x/2 = 256/2
x = 128

So the solution to the equation is x = 128.