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Grade 7 Math: 1.5 Chap.1 Factors and Exponents – Lesson #3 P. 16-17 Powers *Would you rather take $100 000 cash OR take one dollar the first day and triple it everyday for 11 days days? (Re-visit at end of class) Power: a numerical __numerical expression_____ that shows __repeated_____ multiplication. (also known as a number written in exponential form Eg. 5 x 5 x 5 x 5 = 54 Exponent Base Base: the _factor_____ you multiply. Exponent: the number of factors you multiply. (the number of times you repeat the base as a factor) Practice: Write each repeated multiplication as a power. a) 3 x 3 = ____32_ b) 9 x 9 x 9 = __93 Write the following power as repeated multiplication: 63 = __6 x 6 x 6_____ Standard Form: the solution to a power. Eg : 63 = _216____ Naming powers: 45 is a power, which includes a base and an exponent, and can be named: four to the fifth power four to the exponent five the fifth power of four. 45 can be written as repeated multiplication: 4 x 4 x 4 x 4 x 4 and then evaluated or solved and written in standard form: 1024. Try this: Write 74 in words, in three ways: _Seven to the fourth, seven to the exponent four and the fourth power of seven. Square Number: the ____product________ of ___two_______ equal factors. Eg. 16 is the square of 4, since 4 x 4 = 16 or 42 = 16 42 is read as four squared. Area of a square: A = s2 Cubic Number: the ___product______ of __three___________ equal factors. Eg. 8 is the cube of 2, since 2 x 2 x 2 = 8 or 23 = 8 23 is read as two cubed. Volume of a cube: V = s3 Grade 7 Math: 1.5 Writing a number as a power of a given base factor: If you are given a number and then are asked to write it as a power of another number: Eg. Write 243 as a power of 3 (243 is the solution to the power, the base must be 3, raised to some exponent value which must be calculated) 1. Use repeated division method: 1 3 3 Divide 3 into 243, write the answer above 243, then divide 3 into 81, 3 9 write the answer above 81, then divide 3 into 27 ….. until the answer 3 27 becomes 1. The number of 3’s used as the divisor becomes the 3 81 exponent to be placed on the base of 3. 3 243 So 243 written as a power of 3: 243 = 35 2. Use repeated multiplication method: 243 = 3 x 3 x 3 x 3 x 3 = 9x3x3x3 Multiply the base factor “3” by itself as many times as needed to arrive at the product of 243. = 27 x 3 x 3 = 81 x 3 = 243 Try This: Write 256 as a power of 4: 44 *Would you rather take $100 000 cash OR take one dollar the first day and triple it everyday for 11 days? (Re-visit at end of class) Day Repeated Power Prize ($) Multiplication 1 3 31 3 2 2 3x3 3 9 3 3 3x3x3 3 27 4 4 3x3x3x3 3 81 5 5 3x3x3x3x3 3 243 6 3x3x3x3x3x3 36 729 7 7 3x3x3x3x3x3x3 3 2187 8 8 3x3x3x3x3x3x3x3 3 6561 9 9 3x3x3x3x3x3x3x3x3 3 19683 10 3x3x3x3x3x3x3x3x3x3 310 59049 11 11 3x3x3x3x3x3x3x3x3x3x3 3 177147 Grade 7 Math: 1.5 Assignment: P.18-19 # 5, 6, 7 AD, 9 DEF, 12, 13, 17, 19 Bonus #20 Due: __________________