Solve the following equation with a rational exponent: 2x^3/2=16.(1 point)

8

84

4

no solution

1 answer

To solve the equation, 2x^(3/2) = 16, we can start by isolating the variable x.

Divide both sides of the equation by 2:
x^(3/2) = 8

Next, we can rewrite the equation using a fractional exponent:
(sqrt(x))^3 = 8

Now, take the cube root of both sides to eliminate the exponent:
(sqrt(x)) = 2

Square both sides to solve for x:
(sqrt(x))^2 = 2^2
x = 4

Therefore, the solution to the equation is x = 4. So the correct answer is 4.