Exponential Properties Involving Quotients

Key Questions

  • What is the quotient of powers property?

    (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 !!!!!

    Gió · 5 · Dec 19 2014
  • What is the power of a quotient property?

    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)

    Gió · 3 · Dec 25 2014
  • How do you simplify expressions using the quotient rule?

    The Quotient Rule for Exponents

    Let me give you a basic explanation:

    Lets take the example of
    4^36/4^21

    The quotient rule states that for an expression like x^a/x^b = x^(a-b)

    Now of course you question how to simplify expressions using this rule.

    Now lets take such a eg.

    Compute the following: {625x^23}/{25x^3}

    this nothing but 25(x^(23-3))

    So we are left with this final answer 25x^20

    Sidharth · 1 · Jan 24 2015

Questions

Exponents and Exponential Functions