What is the quotient of powers property?

1 Answer
Gió
Dec 19, 2014

#(a^m)/(a^n)=a^(m-n)#

This property allows you to simplify problems where you have a fraction of the same numbers ( #a#) raised to different powers (#m and n#).
For example:

#(3^3)/(3^2)=(3*3*3)/(3*3)=3^(3-2)=3#

You can see how the power of 3, in the numerator, is "reduced" by the presence of the power 2 in the denominator.

You can also check te result by doing the multiplications:

#(3^3)/(3^2)=(3*3*3)/(3*3)=27/9=3#

As a challenge try to find out what happens when #m=n# !!!!!

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