Raising a Product or Quotient to a Power
It is important to know some general rules about exponents:
In radical notation, these properties are written as
Exponent Rule #1
Whenever you multiply terms of the same base, you can add the exponents.
( x m ) ( x n ) = x( m + n )
Note: You cannot add the exponents in this case: (x4)(y3) because x and y are different base terms.
Exponent Rule #2
Whenever you have an exponent expression that is raised to a power, you can multiply the exponent and power:
( xm ) n = x m n
- Simplify (Note the "squared" applies to both x and y).
Exponent Rule #3
Anything to the power of zero is one.
Exponent Rule #4
If you are dividing quantities with the same base term, you can subtract the exponents.
Exponent Rule #5
These are the basic rules, although there are many more laws of exponents that stem from these.