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1. Exponents Curator: K.L Morweng 2. Daily applications Imagine folding a paper once, then twice, the thrice etc. How many subsections of that paper would you get? Imagine winning the Lottery worth that many zeros. Evolution of space storage i.e Memory cards, Hard drives etc. 1MB= 1 x 106 bytes 1GB= 1 x 109 bytes 3. Mathematical definition of exponents An “abbreviation” or shortened form of representing or expressing a very large number or a very small number. a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression. The exponent of a number says how many times to use that number in a multiplication. 4. Exponential Notation Exponential notation refers to repeated multiplication Exponential notation is usually very useful when the same number is repeatedly multiplied. 9 x 9 = 92 1 x 1 x 1 x 1 x 1 x 1= 16 The number being repeatedly multiplied is the base and the exponent tells us how many times our base has been multiplied. Exponent Base 5. Special case 1 “Squared” exponents The number with the exponent 2 is referred to as the “square” of that number 52 Five squared. The square can be used in other dimensions such as measuring the Area of a shape. E.g. Calculate the area of a square whose side is 5m. A = side x side = 5m x 5m = 25m2 (25 meters squared) 6. Special case 2 “Cubed” exponents A number with an exponent of three (3) is referred to as a “cube” of the base. 53 Five cubed The cube can be used in other dimensions such as measuring the Volume of a shape. E.g. Calculate the volume of a square whose side is 5m. V = side x side x side = 5m x 5m x 5m = 125m2 (125 meters cubed) The square and cube of a whole number is referred to as a “perfect square” 7. Rules The invisible exponent When a number or expression does not have a visible exponent, the exponent is 1. 1 xx 8. Exponent rule #1 (Product rule) When multiplying two numbers or expressions with the same base, we ADD their exponents. For example mn b 42 xx 42 x 6 x 2 22 21 22 21 2 3 2 8 9. Exponent rule #2 (Quotient rule) When dividing two expressions with the same base you subtract their exponents. For example m n a a mn a - 2 5 x x -25 x 3 x 10. Continue… Try it on your own: m n a a mn a - 2 6 h h -26 h 4 h 3 33 -13 3 2 3 9 11. Exponent rule #3 (Power rule) When raising a power to a power you multiply the exponents For example: 32 )2( 32 2 6 2 64 mn b )( mn b 42 )(x 42 x 8 x 12. Continue… Try it on your own 23 )(k 23 k 6 k 22 )3( mn b )( mn b 22 3 4 3 81 13. Note!!! When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You would have to use FOIL in these cases 44 2x222 )2( x 14. Exponent rule #4 When a product is raised to a power, each piece is raised to the power Example: m ab)( mm ba 2 )(xy 22 yx 2 )52( 22 52 254 100 15. Continued… Try it on your own: 3 )(hk 2 )32( m ab)( mm ba 33 kh 22 32 94 36 16. Note!!! This rule is for products only. When using this rule the exponent can not be brought in the parenthesis if there is addition or subtraction You would have to use FOIL in these cases 2 )2( x 22 2x 17. Exponent Rule #5 Try it on your own m b a m m b a 2 .9 k h 2 2 k h 2 2 4 .10 2 2 2 4 4 16 4 18. Zero Exponent When anything, except 0, is raised to the zero power it is 1. For example 0 a 1 ( if a ≠ 0) 0 x 1 ( if x ≠ 0) 0 25 1 19. Zero Exponent Try it on your own 0 a 1 ( if a ≠ 0) 0 .11 h 1( if h ≠ 0) 1 0 0.13 undefined 0 100.12 20. Negative Exponents If b ≠ 0, then For example: -n b n b 1 -2 x 2 1 x -2 3 2 3 1 9 1 21. Sources: Heywood, R (2009) Exponent Power Point . Available from Slideshare at https://www.slideshare.net/rheywood/exponent-power-point (Accessed 14 September 2017) Makhanda, O (2014) Basics about exponents. Available from Slideshare at https://www.slideshare.net/oneill0205/basics-about-exponents?qid=8e51a4ad-4d2c-4ca1-8dc6- 010590bf2d12&v=&b=&from_search=1 (Accessed 13 September 2017). McDonald (2010) Exponents in Real Life. Available from Slideshare at https://www.slideshare.net/MrMacD/exponents-in-real-life (Accessed 14 September 2017) Phillips, G (2012) Exponent rules. Available from Slideshare at https://www.slideshare.net/genny_simpson/exponent-rules-12027519?qid=3e09689b-a929-4627- 8c79-83a659b0bc82&v=&b=&from_search=2 (Accessed 10 September 2017). Watt, R (2009) Nov. 19 More Exponent Rules. . Available from Slideshare at https://www.slideshare.net/RyanWatt/nov-19-more-exponent-rules?qid=fb261152-c0b7-4b96- 8eb2-c4fecb740b20&v=&b=&from_search=1 (Accessed 10 September 2017).
