1. Exponents Math 100 Ms. Edna Reyes. 28 June 2010

2. Announcements Starting today all materials will just be posted on the Student Portal Chapter Test on Thursday July 5 – Operations on Signed Numbers – Order of Operations – Fractions and Percentages – Exponents and Roots

3. Exponents If a is any real number and n is a positive integer, then a n = a · a · a … a (n factors of a) E.g. 2 5 = 2 · 2 · 2 · 2 · 2 n Terminology: n is the exponent a is the base a n is the n th power of a

4. Rules of Exponents If a and b are two real numbers; m and n are two integers, then: 1. a m · a n = a m+n 3 1 · 3 2 = 3 3 = 27 2. ( a m ) n = a mn (5 2 ) 3 = 5 6 = 15,625 5 5 = 5 5-3 = 5 2 = 25 3a. a m = a m-n if m>n a n 5353 anan a n-m 3b. a m = 1 if m<n 5 3 = 1 = 1 = 1 5 5 5 5-3 5 2 25 5 4 = 5 4-4 = 5 0 = 1 3c. a m = 1 if m=n a n 5454

5. Rules of Exponents 4. (ab) n = a n b n (3x) 2 = 3 2 x 2 = 9x 2 5. a n = a n b b n () () 3 2 = 3 2 4 4 2 = 9 16 6. a 0 = 1 as long as a= 0 7 0 = 1 / 7. a -n = 1 as long as a= 0 a n 8 -2 = 1 8 2 = 1 64 / 8. a 1 = a as long as a= 0 44 1 = 44 /

6. Others A negative number a with an even exponent is positive A negative number a with an odd exponent is negative (-5) 2 = (-5)(-5) = 25 (-5) 3 = (-5)(-5)(-5) = -125