Question

How do you simplify `(x+3)^(1/3) - (x+3)^(4/3)`?

Answer 1

`- (x+3)^(1/3) * (x + 2)`

Explanation:

You can simplify this expression by using `(x+3)^(1/3)` as a commonfactor.

Focusing solely on the exponents, you need to find the relationship between `1/3`, the exponent of the first term, and `4/3`, the exponent of the second term, so that

`1/3 + color(red)(x) = 4/3 implies color(red)(x) = 4/3 - 1/3 = 3/3 = 1`

If you use `(x+3)^(1/3)` as a common factor, you can thus write

`(x+3)^(1/3) * [1 - (x+3)^(3/3)] = (x+3)^(1/3) * [1 - (x+3)^1]`

`=(x+3)^(1/3) * (1 - x - 3)`

`= color(green)(- (x+3)^(1/3) * (x + 2))`