Warm UP:  Factor:  1) 4v 2 – 4v – 82) 3p 2 – 2p – 5   3) 5n n + 124) 2n 2 + 5n + 2

Exponent Rule Review

Evaluating exponents: find the answer!  (-2) 5 = (-3) 2 = -3 2 =  **Be CAREFUL of where the negative is! Why? ___________________________________________ __________________

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: 3x 3 + 4x 3 = -3c 5 – 7c 5 = 6p 2 – 12 p 2 =  Now, for the rest of the rules

Multiplication with exponents:  If we write out what the question is asking, we would see this:  r 3 ∙ r 2 = (r ∙ r ∙ r) ∙ (r ∙ r) >>>How many total r’s do we see? 5! So, our answer would be r 5.  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: q 4 ∙ q 6 = w 5 ∙w 2 = v ∙v 4 = m 2 ∙ m 3 ∙m 7 =

Exponent of an Exponent  To write out the following: (f 4 ) 2, the 2 means we would write f 4 twice, f 4 ∙ f 4. Using the last rule we learned, the two exponents would add together for a total of f 8. What can we do with the original two exponents, 4 and 2, to make 8? We would multiply them!  The Rule: When you have two exponents together, you multiply them.  EX: (d 3 ) 4 = (s 5 ) 3 = (h 7 ) 8 = (k 6 ) 11 =

ZERO EXPONENT  ANYTHING to the ZERO power is 1 ! Always. Never changes!

Division  Let’s write out and simplify the following what’s left? What can we do with the original exponents, 10 and 4, to make 6? We could subtract them! The Rule: When we are diving with exponents, we subtract the exponents!

Negative Exponents  CAREFUL!!!!!!!! NEGATIVE exponents NEVER NEVER NEVER NEVER NEVER NEVER NEVER make NEGATIVE answers!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!  Yes, that is important and sometimes gives us trouble, so highlight this!  Okay, so, remember scientific notation? 4.3 x vs 4.3 x ? 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).  NEGATIVE exponents take the reciprocal (or flip) of the number! Once we have done the reciprocal, we DROP the NEGATIVE!