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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