Solve the following equation with a rational exponent: 2x^3/2=16.(1 point)
8
84
4
no solution
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.
To solve the equation 2x^(3/2) = 16, we need to isolate the variable x.
First, divide both sides of the equation by 2:
(2x^(3/2))/2 = 16/2
x^(3/2) = 8
Now, we need to eliminate the rational exponent by raising both sides of the equation to the reciprocal of the exponent (2/3 in this case):
(x^(3/2))^(2/3) = 8^(2/3)
x^(3/2 * 2/3) = 8^(2/3)
x^1 = 8^(2/3)
Simplifying the exponents:
x = 8^(2/3)
To calculate 8^(2/3), raise 8 to the power of 2/3:
x = (8^2)^(1/3)
x = 64^(1/3)
Now, find the cube root of 64:
x = ∛64
Since the cube root of 64 is 4, the solution to the equation is x = 4.
Therefore, the correct answer is 4.