Question

How do you simplify `x^(2/3)(x^(1/4) - x)`?

Answer 1

`x^(11/12)-x^(5/3)`

Explanation:

We can distribute the `x^(2/3)` term across the bracketed terms:

`x^(2/3)(x^(1/4)-x)`

`x^(2/3)xxx^(1/4)-x^(2/3)xxx`

Let's first note that `x=x^1`

`x^(2/3)xxx^(1/4)-x^(2/3)xxx^1`

Let's also remember that when multiplying numbers with the same base, we add exponents, i.e. `x^a xx x^b = x^(a+b)`:

`x^(2/3+1/4)-x^(2/3+1)`

And now we combine fractions the way we always do (i.e. make the denominators the same)

`x^(2/3(4/4)+1/4(3/3))-x^(2/3+1(3/3))`

`x^(8/12+3/12)-x^(2/3+3/3)`

`x^(11/12)-x^(5/3)`