What is the power of a quotient property?

1 Answer
Gió
Dec 25, 2014

The Power of a Quotient Rule states that the power of a quotient is equal to the quotient obtained when the numerator and denominator are each raised to the indicated power separately, before the division is performed.
i.e.: #(a/b)^n=a^n/b^n#
For example:
#(3/2)^2=3^2/2^2=9/4#

You can test this rule by using numbers that are easy to manipulate:
Consider: #4/2# (ok it is equal to #2# but for the moment let it stay as a fraction), and let us calculate it with our rule first:
#(4/2)^2=4^2/2^2=16/4=4#
Let us, now, solve the fraction first and then raise to the power of #2#:
#(4/2)^2=(2)^2=4#

This rule is particularly useful if you have more difficult problems such as an algebraic expression (with letters):
Consider: #((x+1)/(4x))^2#
You can now write:
#((x+1)/(4x))^2=(x+1)^2/(4x)^2=(x^2+2x+1)/(16x^2)#

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