(4x)^2/3=(30x+4)^1/3

please explain=)

(4x)^(2/3) = (30x+4)^(1/3)

To do this, note that it's much easier to work with whole number exponents. This we raise both side terms by 3, so that the denominator 3 will be cancelled:
(4x)^(2/3 * 3) = (30x+4)^(1/3 * 3)
(4x)^2 = (30x+4)^1
16x^2 = 30x + 4
Solving for x,
8x^2 - 15x - 2 = 0
(8x + 1)(x - 2) = 0
x = 2
x = -1/8
Then we check by substituting these x values to the original equation:
i. x = 2
(4x)^(2/3) = (30x+4)^(1/3)
(4*2)^(2/3) = (30*2+4)^(1/3)
(8)^(2/3) = 64^(1/3)
2^2 = 4
4 = 4
Thus x is indeed equal to 2.

ii. x = -1/8
(4x)^(2/3) = (30x+4)^(1/3)
(4*(-1/8))^(2/3) = (30*(-1/8)+4)^(1/3)
(-1/2)^(2/3) = (-15/4 + 16/4)^(1/3)
(1/4)^(1/3) = (1/4)^(1/3)
Thus x is also equal to -1/8.

Hope this helps~ :3

i didn't get how 16x^2 turned into 8x^2

16x^2 = 30x + 4
Solving for x,
8x^2 - 15x - 2 = 0

To solve the equation (4x)^(2/3) = (30x+4)^(1/3), we need to isolate the variable x.

Step 1: Raise both sides of the equation to the power of 3. This will eliminate the fractional exponents.
[(4x)^(2/3)]^3 = [(30x+4)^(1/3)]^3

Step 2: Simplify the exponents on both sides.
[(4x)^2] = [(30x+4)^1]

Step 3: Expand and solve the resulting equation.
16x^2 = 30x + 4

Step 4: Set the equation equal to zero by subtracting 30x and 4 from both sides.
16x^2 - 30x - 4 = 0

Step 5: Factor the quadratic equation or use the quadratic formula to find the values of x.
To factor the equation, we can look for two numbers that multiply to -64 (-4 * 16) and add to -30. By trial and error, we can find that the numbers are -32 and +2. Therefore, the equation can be factored as follows:
(4x - 2)(4x + 32) = 0

Using the Zero Product Property, we set each factor equal to zero and solve for x:
4x - 2 = 0 or 4x + 32 = 0

For the first equation, adding 2 to both sides:
4x = 2
Dividing both sides by 4:
x = 1/2

For the second equation, subtracting 32 from both sides:
4x = -32
Dividing both sides by 4:
x = -8

Therefore, the solution to the equation (4x)^(2/3) = (30x+4)^(1/3) is x = 1/2 or x = -8.