Factor the following completely: 1) 3n2 – 20n + 12 2) 6m2 – 7m – 3 3) b2 – 16 4) 14n2 + 50n + 24 5) 16v2 – 9 6) x2 + 4

Be CAREFUL of where the negative is! Why? Aim # 5.0: What are the exponent rules? Evaluating exponents: find the answer! (-2)5 = -2∙-2∙-2∙-2∙-2 = (-3)2 = -3 ∙-3 = -32 = -(3∙3) = Be CAREFUL of where the negative is! Why?

Aim # 4.1: What are the exponent rules? Adding and Subtracting: When we add or subtract terms with exponents, the exponents have to be the SAME and DO NOT CHANGE! We only add or subtract the coefficient. EX: 3x3 + 4x3 = -3c5 – 7c5 = 6p2 – 12 p2 =

What are the rules for multiplying? Multiplication: If we write out what the question is asking, we would see this: r3 ∙ r2 = (r ∙ r ∙ r) ∙ (r ∙ r) How many total r’s do we see? 5 So, our answer would be _____. What could we have done with the 2 & 3 in the beginning of the problem to get our answer? Add them! The Rule: When MULTIPLYING terms, we ADD exponents. EX: q4 ∙ q6 = ___ w5 ∙w2 = ___ v ∙v4 = ___ m2 ∙ m3 ∙m7 =___ 

What is the rule for raising a power to an exponent? Exponent of an Exponent: To write out the following: (f 4)2, the 2 means we would write f4 twice, f4 ∙ f4 which equals… What can we do with the original two exponents? The Rule: When you have a power raised by an exponent, you multiply both exponents. EX: (d3)4 = (s5)3 = (h7)8 = (k6)11 =

What is a number raised to the zero power equal? ANYTHING to the ZERO power is 1 ! Always. Never changes!

What are the rules for dividing powers? Division: Let’s write out and simplify the following: = what’s left? t6. What can we do with the original exponents, 10 and 4, to make 6? The Rule: When we are dividing powers, we subtract the exponents! EX:

What are the rules for negative exponents? NEGATIVE exponents NEVER NEVER NEVER NEVER NEVER NEVER NEVER make NEGATIVE answers. Remember scientific notation? 4.3 x 1044 vs. 4.3 x 10-44? The first is a very LARGE number. The second is a very SMALL (NOT NEGATIVE!) number, right? So, negative exponents are another way of writing very small numbers! We can NEVER have NEGATIVE exponents in our answers! (unless we are asked for scientific notation).

What are the rules for negative exponents? NEGATIVE exponents take the reciprocal (or flip) of the number! Once we have done the reciprocal, we DROP the NEGATIVE! Ex:

Summary: Answer in complete sentences. How do the rules for multiplying powers and dividing powers differ? And how are they the same? Explain how to simplify a power with a negative exponent. Give an example of this.