Solve the following equation with a rational exponent: 5x^4/3=80
.(1 point)
Responses
40.32
16
12
8
To solve the equation 5x^(4/3) = 80, we need to isolate x.
First, we can divide both sides of the equation by 5 to get x^(4/3) = 16.
Next, we can raise both sides of the equation to the power of 3/4 to get rid of the rational exponent. This gives us (x^(4/3))^(3/4) = 16^(3/4).
Simplifying both sides, we have x = 16^(3/4).
To calculate 16^(3/4), we can raise 16 to the power of 3 and then take the fourth root.
16^3 = 4096
Then, taking the fourth root of 4096, we get x ≈ 16.
Therefore, the solution to the equation is x ≈ 16.
To solve the equation 5x^(4/3) = 80, follow these steps:
Step 1: Divide both sides of the equation by 5
(5x^(4/3))/5 = 80/5
x^(4/3) = 16
Step 2: Convert the rational exponent to a radical form
Since the exponent 4/3 can be written as (4th root of x)^3, we have:
(4th root of x)^3 = 16
Step 3: Take the cube root of both sides to eliminate the exponent
4th root of x = ∛(16)
Step 4: Simplify the right side of the equation
∛(16) = 2
Step 5: Raise both sides of the equation to the 4th power to eliminate the 4th root
(4th root of x)^4 = 2^4
x = 16
Therefore, the solution to the equation 5x^(4/3) = 80 is x = 16.