1. 8.2 P.O.D. Simplify the following expressions. 1.2(y 2 ) 5 2. 3x 3 + 2x 3 3. (2x)(4x 2 )(-10x 3 ) 4. 3(x 3 ) 5 5. -3x 2 + x 4

2. Quotients of Powers Section 8.3

3. Big Idea Because of the relationship between multiplication and division, quotients of powers can be themselves written as powers Goal Develop and apply the Quotient of Powers Property

4. HW Answers 8.2

5. Quotient of Powers By expanding the exponent and cross cancelling you can simplify division of powers. EX: Can you think of a short cut to get the same result?

6. Quotient of Powers Rule: for all non zero b, if you divide two powers with the same bases, you can subtract the exponents.

7. REMEMBER – Coefficients still need to be divided not SUBTRACTED

8. 1) Change the following to a simplified power: a.b. c. 4 12-3 = 4 9 4 3-12 = 4 -9 5 13-13 = 5 0 = 1 8.3

9. 2) In March, 1992, there was a total of 283.9 billion dollars in U.S. currency in circulation. The U.S. population was about 252.7 million. how much currency per person was in circulation? ≈ 1.12347 x 10 3 ≈ $1,123.47 per person 8.3

10. 3) Simplify a) b) c) d) = 4x 5 4·10 -3 = 8.3

11. Quiz Review: 8-1 through 8-3 1) Fill in the blank with properties of exponents (includes the Quotient of a powers property) a) b m ∙ b n = b) (b m ) n = c) = b m-n d) 49500000 = scientific notation e) 4.394 x 10 -6 = b m+n bm·nbm·n b m /b n 4.95 x 10 7 0.000004394 Rev1

12. 2) Simplify an expression. Simplify coefficients, use properties = 2x 4-3 y -7+3 z 5+4 = 2xy -4 z 9 = Cancel coefficients, use properties x 4+1-1 y -5-2 z 1-(-4) x -1-2 y 3 z 1-(-3) = Rev1 Simplified expressions have no negative exponents

13. A lot of examples to try:

14. Practice