how does y=x^3/2 become y^2/3=x
I think you can raise both sides to the power of 3/2.
YES : ) If you re-arrange and get x all by itself it truly does equal y^(2/3)
The steps would have been...
1) square both sides
2) take the cube root of both sides
To understand how y = x^(3/2) turns into y^(2/3) = x, we need to apply the process of raising both sides of an equation to a power.
Starting with the original equation: y = x^(3/2)
Step 1: Raise both sides to the power of 2/3.
(y^(2/3))^(3/2) = (x^(3/2))^(2/3)
Step 2: Simplify both sides.
y^(2/3 * 3/2) = x^(3/2 * 2/3)
y^1 = x^1
y = x
So, by raising both sides of y = x^(3/2) to the power of 2/3, we end up with y^(2/3) = x.