Warm Up Find the pattern & the next term of each sequence 25, 5, 1, …. 12, 3, -6, … 0.01, 0.1, 1, … -4, 8, -16, …

Homework Check - 6.1 1) X = -11/6 2) -18 3) Independent – time spent studying Dependent – final exam score 4) m = 1 5) X < -5 6) (10+6)y or 16y 7) Y = 2x + 5 8) X = -5/8

Unit 6 – Day 2 Properties of Exponents Take out a sheet of paper for today’s notes/practice..

Exponent Rules Review Exponents are a “short-hand” way of multiplying the same quantity over and over. Example: What does X4 mean?

Try Some: Expand the following 43 Y4 X2y5 w6z1

Using Exponents to simplify Write using exponents x*x*x*x 2*2*2*2*x*x*x*y*y 3*3*3*4*4*4*4*x

Zero as an exponent Anything with an exponent of zero equals 1. (Check this in your calculator) Ex) x0 = 1 60 = Y0 =

Negative Exponents When you have a NEGATIVE exponent you turn it POSITIVE and FLIP it. EX x-3

Try Some

Multiplication When multiplying like bases you ADD exponents Ex) x4x2

Try some! X3x4 Y3x4y7 z3y2x5z5y6x10

Power to a Power Rule When you have an exponent of an exponent you MULTIPLY the exponents EX: (x4)3

Try Some! (x)5 (x2y4)5 (2x3)6

Division When you divide like bases you SUBTRACT exponents

Try Some

Growing Sequences Arithmetic Sequence: goes from one term to the next by always adding (or subtracting) the same value Common Difference : The number added (or subtracted) at each stage of an arithmetic sequence Initial Term : Starting term For example, find the common difference and the next term of the following sequence: 3, 11, 19, 27, 35, . . .

Growing Sequences Geometric Sequence: goes from one term to the next by always multiplying (or dividing) by the same value Common Ratio: The number multiplied (or divided) at each stage of a geometric sequence Determine the common ratio r of the Brown Tree Snake Sequence. 1, 5, 25, 125, 625, . . .

Practice with Sequences

HW 6.2