19+-+Sec.+8.3B

**Section 8.3 B** Division properties of exponents: Quotient of powers and power of a quotient
By: Ronnie Snyder, Caitlin Remmey, and Alec Spece


 * __Main Idea:__**


 * Quotient of powers property:** The property says, to divide powers having the same base, subtract the exponents.

__a^m__= a^m^-n, a=0 a^n


 * Power of a quotient property**: The property says, that the power of a quotient can be found by finding the powers of the numerator and denominator, keeping as a fraction. (Sprinkling)


 * (**__a__**)**^m = __a^m__ b=0
 * (**b**)**^m b^m

**Links:**
[|Quotient of Powers and Power of Quotient Mathematics]

[|Interactive Review] (Open in full show, each click of the mouse reveals and answer)


 * Examples:**

-The division problems are just like subtracting and multiplication problems is just like adding when doing these problems.
 * 1) X^6 / X^2= X^4
 * 2) X^5/ X^4= X^1
 * 3) X^9/ X^4= X^5
 * 4) (y/z)^3 = y^3/z^3
 * 5) (xy^3/y)^6 = x^6y^18/y^6 = x^6 y^12
 * 6) (xy^2/y)^5 = x^5y^10/y^5 = x^5 y^5

**Practice Problems:**
1. Simplify ( __3x__^5)^3 ( 7y^2)

2.Simplify (__xy^4__)^8 (y^2)

3. (__-5xy^8__)^3 (5xy^4)^2