If the problem provides a term that contains a negative exponent, you need to use the following identity:

Hence, using the formula above, you may evaluate any negative power given.

Use the following as an example: Considering

If you raise a number to a negative power, it is like saying that it is that number but as the denominator of a fraction. So, in other words, if you have x^-2, that is the same thing as saying 1/x^2.

So if some number is raised to a negative power, you have to make it into a fraction.

The negative power is following the rule:

a^-b = 1/a^b

As we can remark, the negative power moves the base "a", to the denominator.

But why is that?

We know that the difference between 2 exponents means the division between 2 powers that have like bases.

For example:

5^8/5^3 = 5^(8-3) = 5^5

In the first example,we've written:

a^-b = 1/a^b

We can see a^-b = a^(0-b) = a^0/a^b

But, according to the rule, any number raised to zero exponent, is equal to 1.

So, a^0 =1

That's why a^-b = 1/a^b, because 1 = a^0.