This document discusses negative exponents and how to simplify expressions with negative and fractional exponents. Some key points: 1) A zero exponent evaluates to 1, so b0 = 1 for any nonzero real number b. 2) For a negative exponent b-n, where b is a nonzero real number and n is a positive integer, b-n = 1/bn. 3) Examples are provided of simplifying expressions using negative exponent rules, such as reducing 3x-4 to 1/(3x)4 when x = -2. 4) Expressions with mixed negative, positive, and fractional exponents can be simplified to expressions with only positive exponents.

1. 6.4 Negative ExponentsObjective: To simplify expressions with integral exponents

2. To evaluate monomials with integral exponentsFrameworks: 10.P.1, 10.P.7

3. What is 50?53 = 53-3 = 50 = 153A zero exponent evaluates to 1

4. Zero ExponentFor each nonzero real number b,b0 = 1 (00 is undefined.)

5. Try some: (x ≠ 0)4x0(5x)0xy0(7x6)0

6. What about a2/a5?a * aa * a * a * a * a = 1/(a * a * a) = a-31 = 1x-3 = 1x3= x3

7. Negative ExponentFor each nonzero real number b and for each positive integer n,b-n= 1 and 1 = bnbn b-n

8. Try some:35* 3-8(ab-7)(-b-3)Evaluate 3x-4 for x = -2

9. Simplify using only positive exponents:(x-8y-5)(x10y-2)

10. Simplify using only positive exponents:3x-57y-2