Question

How do you simplify `(-243)^(3/5)`?

Answer 1

-27

Explanation:

With this type of question, see that an exponent in the form of `a/b` means that we should take the base number to the `a` power and also take the `b`th root.

In our case, we're being asked to take -243 to the 3rd power and also to take the 5th root. This will be easier if we first see that:

`-243=(-3)^5`

And so we can rewrite our question as

`(-243)^(3/5)=((-3)^5)^(3/5)`

We can now apply the rule that

`(x^a)^b=x^(ab)`

`((-3)^5)^(3/5)=(-3)^(5xx(3/5))=(-3)^3=-27`