Exponential Notation 1-3

I. Using Exponents A. Vocabulary: Power – product in which the factors are the same Exponent – tells how many times the base is multiplied Base – the number that is multiplied Exponential notation – an expression that is written with exponents

B. Writing out an expression with exponential notation: 22 = 2 x 2 35 = 3 x 3 x 3 x 3 x 3 n4 = n x n x n x n y3 = y x y x y 2y3 = 2 x y x y x y (the exponent is only connected to the y, so that is the only thing that is expanded)

Examples: 1. 54 2. b3 3. 2x3 4. 12y4

C. Writing in exponential notation: 7 x 7 x 7 x 7 = 74 n x n x n x n x n x n = n6 3 x m x m = 3m2 2 x y x y x y x y = 2y4

Examples: 1. 9 x 9 x 9 2. y · y · y · y · y 3. 4 x n x n x n x n x n 4. 15 · x · x · x · x 5. 10 x b x b x b

You can also “evaluate” problems that include exponents Note: You can also “evaluate” problems that include exponents ex. y4 + 3 for y = 2 24 + 3 2 · 2 · 2 · 2 + 3 16 + 3 = 19 End of Part 1

II. Exponents with Parentheses Up until now, all exponents were connected to only one number/variable, known as the base 2y5 When an expression inside parentheses is raised to a power, everything inside the parentheses becomes the base (2y)5

A. To solve problems with exponents on the outside of the parentheses, you must connect/distribute the exponent to everything on the inside 1. (3a)4 2. (5y)3 34 · a4 53 · y3 81 · a4 125 · y3 81a4 125y3

B. You can also do this same thing with evaluating: Example: (4m)3 for m = 2 43 · m3 43 · 23 64 · 8 512

Examples: 1. (10y)2 2. (6m)3 3. (8n)5 for n=2 End of Part 2

C. When you have exponents both inside and outside of the parentheses: You must multiply the exponents (52)3 56 = 15,625 Multiply your exponents

Examples: 1. (84)3 2. (k7)5 3. (3a2)5

III. Exponents in Fractions A. If you have the same base in the top and bottom of the fraction, and they have exponents, you can simplify B. As long as they are the same base, you will take the top exponent and subtract the bottom exponent 35 33 32 Take the exponents and subtract…5 – 3 = 2

Examples: 1. 78 2. b12 3. x 75 b4 x3

C. If you do not have the same base, you cannot subtract the exponents D. If there are multiple bases, combine your like bases and leave the rest where they were x6y2 = x3z4 x3y2 z4 Here are your like bases… subtract the exponents

Examples: 1. 126145 2. a3b8 3. 3xy 124 b2c9 12y