Understanding negative exponents
NEGATIVE EXPONENTS
and
When raising a base to a negative exponent, find the reciprocal of the base.
The definition indicates that negative exponents give us reciprocals, as the following examples illustrate.
Simplify 2^{3}
The first step is to rewrite the expression with a positive exponent, by using our definition. After that, we simplify.


Definition of negative exponents 


The cube of 2 is 8 
Simplify (3)^{2}
The fact that the base in this problem is negative does not change the procedure we use to simplify:


Definition of negative exponents 


The square of 3 is 9 
Simplify
Simplify