Radical Functions: Roots and Properties of Exponents

think icon Think & Click: Analyze Laws of Exponents

Before we look at some examples of problems involving exponents, let's analyze why some of the laws are true.

Work through each of the questions and then click on the question to check your answer.

Why does the Product of Powers Property hold true for exponents?
 

Look at the following expansion of the property.

a to the m power equals a times a times a times a times a…continue this m times(m times)

a to the n power equals a times a times a times a times a…continue this n times(n times)

Therefore if we put them together, aman must be the addition all of the a's which is am+n.
 

Why does the Quotient of Powers Property hold true for exponents?
 

Look at the following expansion of the property.

a to the m power equals a times a times a times a times a…continue this m times(m times)

a to the n power equals a times a times a times a times a…continue this n times(n times)

a to the m power divided by a to the n power equals a times a times a times a times a…m times divided by a times a times a times a…n times

Remember that a divided by a equals one. You can start canceling out the a's in the numerator and the denominator. This is equivalent to a to the m power divided by a to the n power equals a to the m minus n power.