Final answer:
To solve the equation 5(x)^(3/2) = 40, divide by 5 to get (x)^(3/2) = 8, then take the cube root to get (x)^(1/2) = 2 and square both sides to find x = 4, which is the solution.
Step-by-step explanation:
To solve the equation 5(x)^(3/2) = 40, we need to isolate the variable x. First, divide both sides of the equation by 5 to get (x)^(3/2) = 8. Taking the cube root of both sides gives us (x)^(1/2) = 2. To remove the exponent of 1/2, which represents the square root, we square both sides, yielding x = 4. The solution is x = 4.
Let's confirm this solution by plugging it back into the original equation:
- 5(4)^(3/2) = 5(2^3) = 5(8) = 40
This confirms that x = 4 is indeed the correct solution to the equation.