Question

What is the power of a quotient property?

Answer 1

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)`