Question

If `(x-1)^(2/3) =25` then x equals what?

Answer 1

`x=126`

Explanation:

This problem might appear scary because to isolate `x`, you need to so some tricky stuff with exponents.

But if you think about it, we can cancel out the `2/3` by raising each side to `3/2`, because when you raise an exponent to an exponent it serves to multiply the two, and `2/3*3/2=1`.

Based on this, we can raise `25` to the power of `3/2`, as well as `(x-1)^(2/3)` in order to get the equation

`(x-1)^(2/3*3/2)=25^(3/2)`
`(x-1)=125`
`x=126`

Sure enough, if you plug in 126 for `x`, you get `25` as your output:
![https://www.desmos.com/calculator/czkefr2lhb]()