Solve the following equation with a rational exponent: 2x3/2=16.(1 point)

Question

Responses

84
84

4
4

no solution
no solution

8
8

Answer 1

To solve the equation \( 2x^{3/2} = 16 \), we can follow these steps:

1. Isolate the term with the variable: \[ x^{3/2} = \frac{16}{2} \] \[ x^{3/2} = 8 \]

2. Raise both sides to the power of \(\frac{2}{3}\) to solve for \(x\): \[ x = 8^{\frac{2}{3}} \]

3. Calculate \(8^{\frac{2}{3}}\):

   • First, find the cube root of 8: \[ 8^{\frac{1}{3}} = 2 \]
   • Then square the result: \[ (8^{\frac{1}{3}})^2 = 2^2 = 4 \]

So, we find: \[ x = 4 \]

Thus, the solution to the equation \( 2x^{3/2} = 16 \) is: \[ \boxed{4} \]