Exponential Notation 1 3 I Using Exponents A

I. Using Exponents A. Vocabulary: ◦ Power – product in which the factors are

B. Writing out an expression with exponential notation: 22 = 2 x 2 35

C. Writing in exponential notation: 7 x 7 x 7 = 74 n x

Examples: � 1. � 2. � 3. � 4. � 5. 9 x 9

� Note: You can also “evaluate” problems that include exponents ex. y 4 +

II. Exponents with Parentheses � Up until now, all exponents were connected to only

� A. To solve problems with exponents on the outside of the parentheses, you

� B. You can also do this same thing with evaluating: � Example: (4

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

� C. When you have exponents both inside and outside of the parentheses: ◦

Examples: 1. (84)3 2. (k 7)5 3. (3 a 2)5

III. Exponents in Fractions A. If you have the same base in the top

Examples: � 1. 78 75 2. b 12 b 4 3. x x 3

� C. If you do not have the same base, you cannot subtract the

Examples: � 1. 126145 124 2. a 3 b 8 b 2 c 9

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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 n 4 = n x n x n y 3 = y x y 2 y 3 = 2 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. b 3 � 3. 2 x 3 � 4. 12 y 4

C. Writing in exponential notation: 7 x 7 x 7 = 74 n x n x n x n = n 6 3 x m = 3 m 2 2 x y x y = 2 y 4

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

� Note: You can also “evaluate” problems that include exponents ex. y 4 + 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 2 y 5 � When an expression inside parentheses is raised to a power, everything inside the parentheses becomes the base (2 y)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. (3 a)4 2. (5 y)3 3 4 · a 4 5 3 · y 3 81 · a 4 125 · y 3 81 a 4 125 y 3

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

Examples: 1. (10 y)2 2. (6 m)3 3. (8 n)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 Multiply your exponents 56 = 15, 625

Examples: 1. (84)3 2. (k 7)5 3. (3 a 2)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 Take the exponents and subtract… 5 – 3 = 2 33 32

Examples: � 1. 78 75 2. b 12 b 4 3. x x 3

� C. If you do not have the same base, you cannot subtract the exponents m 3 t 5 � D. If there are multiple bases, combine your like bases and leave the rest where they were Here are your like bases… subtract the exponents x 6 y 2 = x 3 z 4 x 3 y 2 z 4

Examples: � 1. 126145 124 2. a 3 b 8 b 2 c 9 3. 3 xy 12 y