How do you simplify # -4^(-5/2)#?
Let's start with the negative exponent.
We can appy the following power rule:
As next, let's take care of the
First of all, the fraction can be split into
Another power rule states:
Here, this means that you can either compute
Let's stick with
So you get
In total, your solution is:
- Make the exponent positive
- A bit of algebra
Let's start off by having a look at the expression. The minus sign is not a part of the base (which is 4), so therefore, we can write the expression like this:
When we have to deal with negative exponents, we have a set of rules that simplyfies them. One of them is:
Another one, that we will use to convert exponents into square roots is:
So let's begin!
We already have
Followed by the rule about exponents into square roots:
Just some algebra that remains!