1. Section 5.2 Quotient Rule and Zero Exponents

2. 5.2 Lecture Guide: Quotient Rule and Zero Exponents Objective 1: Use the quotient rule for exponents.

3. Expanded Form:Alternate form: 1. Complete the warm-up examples below. Assume (in exponential form)

4. Algebraically For any real number x and natural numbers m and n with, m > n, for is undefined for x = 0. Verbally To divide two expressions with the ___________ base, use the common base and __________ the exponents. Algebraic Example ______________ Quotient Rule for Exponents where m > n:

5. 2. 3. Simplify each expression.

6. 4. 5. Simplify each expression.

7. 6. 7. Simplify each expression.

8. Expanded Form: Alternate form: 8. Complete the warm-up examples below. Assume.

9. The expression can also be simplified when m < n. The reasoning is similar to that when m > n. If and m and n are natural numbers, then for m < n. Quotient Rule for Exponents where m < n In the next section, we will examine another way to interpret when m < n.

10. 9. 10. Simplify each expression, assuming all bases are nonzero.

11. 11. 12. Simplify each expression, assuming all bases are nonzero.

12. Objective 2: Simplify expressions with zero exponents. Expanded Form: Alternate form: 13. Complete the warm-up examples below: (in exponential form) (as a reduced fraction) Assume

13. Algebraically For any nonzero real number x,. is undefined for x = 0. Verbally Any ______________ real number raised to the 0 power equals 1. Algebraic Example _______________ Zero Exponents

14. Simplify each expression if possible. 14. (a) (b) (c) (d)

15. 15.16. Simplify each expression, assuming all bases are nonzero.

16. 17.18. Simplify each expression, assuming all bases are nonzero.

17. Objective 3: Combine the properties of exponents to simplify expressions.

18. For any nonzero real numbers x and y and whole number exponents m and n, Product rule: ____________ Power rules: Quotient rule: ____________for m > n ____________for m < n Zero exponent: ____________for is ____________ Summary of the Properties of Exponents

19. Simplify each expression. Assume all bases are nonzero. 19.20.

20. Simplify each expression. Assume all bases are nonzero. 21.22.

21. Simplify each expression. Assume all bases are nonzero. 23.24.

22. 25. Use the formula to find the value of a $15,000 investment compounded at 9% at the end of each year over a six-year period. Year, tValue, A 0$15,000 1 2 3 4 5 6

23. Comparing Subtraction and Division Subtract the like terms and simplify the quotients. Assume 26.27.

24. Comparing Subtraction and Division Subtract the like terms and simplify the quotients. Assume 28. If possible, subtract

25. Comparing Subtraction and Division Subtract the like terms and simplify the quotients. Assume 29. If possible, divide