Zero exponent/Neg. exponent Absent Thurs/Fri 10/31-11/1

Pattern example Zero/Neg. exponent Property 2-1 1 2 20 1 21 2 22 4 23 8 24 16 What Pattern do we see when we are moving down? As the exponent increases by 1 number than the answer doubles itself. What pattern do we see when we are moving up? As the exponent decreases by 1 number than the answer is reduced by half. What does the 2-1 turn into? The Negative exponent turns into a fraction. Neg. exponents always turn into fractions.

Example #1 50 1 Solution Simplify: (3 + 2)0 What can we do first? Use GEMA and add what’s inside the groupings. What happens when there is a exponent of 0? Anytime there is an exponent of 0 then the base (factor) becomes 1 1

Example 2 1 Simplify: -64 What is the base (factor)? The factor is (-4) What is the exponent? The exponent is -3 How do we re-write the problem? We have to write the problem as a fraction because of the neg. exponent. It makes it Positive. What do we do next? Write out the factor in expanded form with ( ). 3 neg signs. Odd # What is the last step? To multiply the factors which are part of the denominator. Simplify: (-4)-3 1 (-4)3 (-4)(-4)(-4) -64 Solution 1 -64

Example 3 -2 = -1 4 2 Simplify: (4)-1 – (3 + 2)0 + (2)-2 1 + -4 + 1 What are the first step? Use GEMA and add what’s inside the groupings. How do we re-write the expression when we have zero’s & neg. exponents? We write all zero exponents as 1 and all neg. exponents as a fraction. What is the next step? We multiply the exponents. What do we have to do first before adding the fractions? We have to get all the denominators to be the same. What's are last step? We can now add all the numerators using the integer rules. Simplify: (4)-1 – (3 + 2)0 + (2)-2 (4)-1 - (5)0 + (2)-2 1 + -1 + 1 (4)1 1 (2)2 1 + -1 + 1 4 1 4 1 + -4 + 1 4 4 4 Solution -2 = -1 4 2

Example 4 Simplify: 3(1 – 4)-2 + (9)-1 + 120 What are the first step? 3(-3)-2 + (9)-1 + 120 3 + 1 + 1 (-3)2 (9)1 1 3 + 1 + 1 9 9 1 3 + 1 + 9 9 9 9 13 9 What are the first step? Use GEMA and add what’s inside the groupings. How do we re-write the expression when we have zero’s & neg. exponents? We write all zero exponents as 1 and all neg. exponents as a fraction. What is the next step? We multiply the exponents. There are 2 neg. signs with the (-3) even #. What do we have to do first before adding the fractions? We have to get all the denominators to be the same. What is the last step? We can now add all the numerators using the integer rules. Reduce the answer. 13 9