X^1/3 - 2/5 = 0

x^1/3 = 2/3
x= 2/3^(1/3)
x=1.38

is that right?

Also

(x-4)^3/2 = -6

How do you do that?

x = 1.38 does not verify your first equation,

if I take the cuberoot of 1/38, I don't get 2/5

I see an error in your second line

x^(1/3) = 2/5
now cube both sides
x = 8/125

for your second, there is no "real" solution.
an exponent of 3/2 means, take the square root, then cube that result
since we cannot take the square root of -6, .......

Reiny, after working it the first 1 over, i got .016

How would u work the second one? can you show me steps by step?

If your first equation is x^(1/3) - 2/5 =0

then
x= (2/5)^3 = (2^3)/(5^3) = (8/125) = 0.064

for your second equation I believe you should do the following:

(x-4)^3/2 = -6
First raise both to the 2/3 power to get rid of the ^3/2.

(((x-4)^3/2)^(2/3)))=(-6)^(2/3)

=>(x-4)=((-6)^(2/3))=> x = ((-6)^(2/3))+4

=> x = 36^(1/3) + 4

did you not read my reply?

I worked out both of your questions
The answer you gave after my post still does not work

use to calculator to find the cuberoot of .016, you would get .25198 which is not equal to 2/5

but the answer I gave you, namely 8/125, has as its cuberoot 2/5

Ahh okay. I didn't get it at first, but now that I read it, I got it. Thanks alot!

Chris, for the second equation there is no solution

Did you verify your answer in the original equation??

that is..
is (7.3019)^1.5 = -6 ????

I think they are two separate questions and since the -6 is on the right sideto find x one would square both sides and find the cube of that result then subtract add four. I could be mistaken.

I think they are two separate questions and since the -6 is on the right sideto find x one would square both sides and find the cube root of that result then add four. I could be mistaken

(x-4)^3/2 = -6

Chris, you can do what you said but it would be wrong.
what you said:
(x-4)^3 = 36
x-4 = 3.3
x = 7.3 HOWEVER
go back and check
3.3^3/2 = +6 NOT -6
In other words, when you squared both sides you threw the problem out with the bath water.

For the first equation, x^1/3 - 2/5 = 0:

To solve for x, we need to isolate the variable.

1. Start by adding 2/5 to both sides of the equation:
x^1/3 = 2/5

2. To eliminate the exponent 1/3, cube both sides of the equation:
(x^1/3)^3 = (2/5)^3
x = (2^3)/(5^3)
x = 8/125
x ≈ 0.064

So the correct solution for the first equation is x ≈ 0.064.

Now let's move on to the second equation, (x-4)^3/2 = -6:

1. Start by raising both sides of the equation to the reciprocal power of 2/3:
((x-4)^(3/2))^(2/3) = (-6)^(2/3)

2. Simplify the left side of the equation:
(x-4)^(3/2 * 2/3) = (-6)^(2/3)
(x-4)^(1) = (-6)^(2/3)
x-4 = (-6)^(2/3)

3. Simplify the right side of the equation:
(-6)^(2/3) = ∛((-6)^2)
(-6)^(2/3) = ∛(36)
(-6)^(2/3) = 3∛(4)

4. Add 4 to both sides of the equation:
x -4 + 4 = 3∛(4) + 4
x = 3∛(4) + 4
x ≈ 3.077

So the correct solution for the second equation is x ≈ 3.077.