Negative Indices

What is a negative indices? A number or term with a negative index means it can be written as a reciprocal of that number. 

For example,

And:

How do we get negative indices?

Negative indices occur when multiplying or dividing two terms where the the result of adding or subtracting the powers gives a negative value.

For example, 

a³ × a^-5 = a^{3 + - 5} = a^-2 = 1/a²

or

p¹ ÷ p² = p^1-2 = p^-1= 1/p