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1. Exponents September 28, 2015 Vocabulary you should know.... Exponents exponent a number that indicates how many times the base is used as a factor. Writing exponents is a shorthand notation to show multiplication. 53 means 5• 5• 5 3 is the exponent. base a number used as a factor in an exponential expression. In the expression 73 , 7 is the base. Special Cases n1 = n any number to the firstpower = itself variable – a symbol or letter that represents a number that can change or is unknown Ex. x, z, r, π, Θ constant a value that does not change (not affected by a variable) Ex. 7, 19, 208 n0 =1 any number to the 0 power = 1 except 00 which is undefined coefficient a factor that is multiplied to a variable Ex. 27y 12x 5n algebraic expression contains one or more variables and may contain operation symbols and constants Ex. 8n, 27x + n, 15y2 Writing algebraic expressions as repeated multiplication When there is no symbol between variables and/or constants it means multiplication. There MUST be symbols between two constants. Variables are written in alphabetical order Ex. x2y3 = coefficients are written before variables Ex. 5x2y3z2 = When variables and/or constants in parentheses are raised to an exponent, everything in the parentheses are raised to that power. Ex. 5n2(xy)3= Try This! First show the extended form of the exponent. Then solve. 54= 1. Exponents September 28, 2015 75= 1451= t8= 23k4= 140= Write the following in exponential form 7 7 7 7 7 7 Θ Θ Θ Θ 1. Exponents September 28, 2015 More Exponents: Squares and Cubes square n2 , raising to the power of 2, multiplying a value by itself. 62 = 6 ∙ 6 = 36 42 = 9 2 = x2 = cube n3 , raising to the power of 3, multiplying three of the same value by itself. 23 = 2 ∙ 2 ∙ 2 = 8 43 = 5 3 = y3 = Square and cube are the only two numbers that have special names. For the rest of the numbers we say.... 1. Exponents Write the following in exponential form, then solve. September 28, 2015 seven squared= fourteen cubed= nine to the 4th power= three cubed plus eleven squared= theta cubed= Clicker Problems for today and yesterday 1. twelve squared 2. nine cubed 3. three squared 4. 52 5. 2 cubed 6. 43 7. 6 to the second power 8. Do you know what a perfect square number is? 1. Exponents September 28, 2015 Perfect Square Numbers Perfect Square Numbers n 1 n2 2 n n2 = n n n2 1 11 2 12 2 3 3 13 4 14 5 15 6 16 4 7 17 8 18 5 9 19 10 20 = n Powers of Ten in Exponential Form n n 1 1 2 4 3 9 4 16 5 25 = n 2 n n2 11 121 = n 100 = 10 ● 10 = 102 one hundred thousand= 100,000 = 10●10●10●10●10 = 105 12 144 13 169 10 14 196 The exponent is the number of zeroes! 15 225 6 36 7 49 8 64 17 289 9 81 18 324 16 256 19 361 10 100 20 400 Practice Write each numeral in exponential form or vice versa a. one trillion 1,000,000,000,000 = 1012 b. 107 10,000,000 c. 10,000,000,000,000,000 d. 109 1,000,000,000 e. 100 quintillion f. 1018 100,000,000,000,000,000,000 = 1020 1,000,000,000,000,000,000 one quintillion g. 10 million h. 1010 = 1016 10,000,000 = 107 10,000,000,000 = ten billion erase to reveal 8 = 100,000,000 = one hundred million 1. Exponents September 28, 2015 Zero as an exponent Any number raised to the zero power is 1, except 00 is undefined.