Laws of Exponents Learning Strategies

Transcription

1 Laws of Epoets Learig Strategies What should studets be able to do withi this iteractive? Studets should be able to uderstad ad use of the laws of epoets. Studets should be able to simplify epressios that have positive, egative, or zero epoets with variable or umeric bases. Commo mistakes made by studets: ot uderstadig the meaig of a epoet as the umber of times a base is repeated i multiplicatio maipulatig the base istead of the epoet ot rememberig that the laws for epoets are shortcuts performed o the epoets, ot the base thikig that egative epoets produce egative results ot distiguishig oe law from aother ot distiguishig the differece betwee a egative umber ad a egative epoet Commo Mistakes Made withi Each Law: For the Product of Powers: m multiplyig the epoets multiplyig or addig the bases m For the Quotiet of Powers: m m dividig the epoets dividig the bases subtractio errors with egative epoets m m For the Power of a Power: ) multiplyig the outer epoet oto both the base ad the ier epoet addig the epoets multiplicatio errors with egative epoets. m m m For the Product of a Power: y) y ot multiplyig the outer epoet oto all of the ier epoets addig the epoets Juior High Math Iteractives Page of 006 Alberta Educatio

2 For the Quotiet of a Power: y y ot multiplyig the outer epoet oto epoets of both the umerator ad deomiator. multiplicatio errors dividig epoets multiplyig the epoet ad the base together 0 For Zero Epoets:, 0 thikig the result of a zero epoet is zero thikig the result of a zero epoet is the value of the base ot uderstadig the meaig of a zero epoet ad where it could arise i a questio ot uderstadig why the result of a zero epoet is always oe For Negative Epoets:, 0 thikig that all egative epoets result i egative aswers ot makig the umerator whe reciprocatig the base ot uderstadig the meaig of a egative epoet forgettig to make the epoet positive after it has bee reciprocated ot distiguishig betwee a egative base ad egative epoet Curriculum Coectios: Please ote all of the followig correlatios match outcomes i the ew Mathematics Kidergarte to Grade 9 Program of Studies 007). Grade 9 Number SO: Demostrate a uderstadig of powers with itegral bases ecludig base 0) ad whole umber epoets by: represetig repeated multiplicatio, usig powers usig patters to show that a power with a epoet of zero is equal to oe solvig problems ivolvig powers. Juior High Math Iteractives Page of 006 Alberta Educatio

3 Grade 9 Number SO: Demostrate a uderstadig of operatios o powers with itegral bases ecludig base 0) ad whole umber epoets: Math 0-C Algebra ad Numbers SO: Demostrate a uderstadig of powers with itegral ad ratioal epoets. Prit Activity otes: *Note: The Prit Activity is ot iteded to be a assessmet piece It is recommeded that studets use the Eplore It mode to work through the Prit Activity. Studets will be asked to eamie each law i its epoetial ad epaded form. The activity will allow studets to see the patters that form the basis behid the rules for the laws. The Prit Activity may be opeed i Word Format istead of PDF so that chages to questios ca be made. Laws of Epoets Prit Activity Key. Use the Product Law i the Eplore It mode for the followig eercise. Move the slider bars as directed: m purple) to orage) to red) to a. Use the above eample i the Eplore It mode to complete the followig: Juior High Math Iteractives Page of 006 Alberta Educatio

4 Epoetial Form Epaded Form )) ))) ) ))))) ) ) b. Complete all the missig parts i the followig table: m Epoetial Form Epaded Form simplified) Eg. ) + = ) ))))) ) ) ) + = ) ))))) ) ) ) ) -)-)-)-) Eg. ) - ) ) -+ = ) )) ) ) ) ) ) ) ) ) - + = ) ) - ) ) c. Complete the Product Law: Whe multiplyig like bases, you must add the epoets.. Use the Quotiet Law i the Eplore It mode for the followig eercise. Move the slider bars as directed: m purple) to orage) to red) to Juior High Math Iteractives Page of 006 Alberta Educatio

5 a. Aswer the followig usig the above eample i the Eplore It mode: Epoetial Form ) ) Epaded Form ))))) ))) ) b. Complete all the missig parts i the followig table: m Epoetial Form Epaded Form simplified) Eg. ) ) ))) ) ) ) ) -) -) ) ) ) -) ) ) ) ) ) ) Eg. ) - ) ) 6 ) ) )))) ) ) ) ) ) ) - -- = ) ) - 6 ) ) )))))) c. Complete the Quotiet Law: Whe dividig like bases, you must subtract the epoets. Juior High Math Iteractives Page of 006 Alberta Educatio

6 . Use the Power of a Power Law i the Eplore It mode for the followig eercise. Move the slider bars as directed: m purple) to orage) to red) to a. Use the above eample i the Eplore It mode to complete the followig: Epoetial Form ) ) Epaded Form ) ) ) ) 6 ) )) )) )) ) b. Complete all the missig parts of the followig table: m ) Epoetial form Epaded formsimplified) eg. ) 6 ) ) )))))) 6 ) ) ) -) ) 6 ) ) -) ) ) ) )))) -)-)-)-)-)-) -)-)-)-) 8 e.g.-) - ) ) ) ) - ) - 6 ) ) )))))) -) - ) - ) ) -)-)-) ) ) - ) ) Juior High Math Iteractives Page 6 of 006 Alberta Educatio

7 c. Complete the Power of a Power Law: Whe raisig a power to aother power, you must multiply the epoets.. Use the Power of a Product Law i the Eplore It mode for the followig eercise. Move the slider bars as directed: m purple) to y gree) to red) to a. Use the above eample i the Eplore It mode to complete the followig: Epoetial form ) ) ) ) ) Epaded form ) ) ) )) )) b. Complete all the missig parts i the followig table: y) m Epoetial form Epaded form e.g. ) ) ) = ) ) ))) ))) ) ) ) ) ) ))) ))) - ) -) ) = ) ) -)-)-) ))) ) - ) ) = ) ) - ) -) ) = -) ) ) ) ) ) ) -)-) )) Juior High Math Iteractives Page 7 of 006 Alberta Educatio

8 c. Complete the Power of a Product Law: Whe fidig the power of a product, you must multiply the epoet outside the bracket by all the epoets iside the bracket.. Use the Power of a Quotiet Law i the Eplore It mode for the followig eercise. Move the slider bars as directed: m purple) to red) to y gree) to a. Use the above eample i the Eplore It mode to complete the followig: Epoetial Form ) ) ) ) Epaded Form ) ) ) ) b. Complete all the missig parts i the followig table: m Epoetial Form Epaded Form y Eg. ) ) ) = ) ) ) ) Juior High Math Iteractives Page 8 of 006 Alberta Educatio

9 ) ) ) = ) ) ) ) ) ) ) ) ) c. Complete the Power of a Quotiet Law: Whe fidig the power of a quotiet you must multiply the epoet outside the bracket by all the epoets iside the bracket. 6. Use the Zero Epoet Law i the Eplore It mode for the followig eercise. Move the slider bar as directed: red) to a. Use the above eample i the Eplore It mode to complete the followig: Epoetial Form 0 Epaded Form 0 ) Juior High Math Iteractives Page 9 of 006 Alberta Educatio

10 b. Complete all the missig parts i the followig table: ) 0 Epoetial form Epaded form e.g. ) 0 ) 0 = = y) 0 y) 0 = -) 0 -) 0 = y y ) ) = c. Complete the Zero Epoet Law: The value of ay base to the zero epoet is. 7. Use the Negative Epoet Law i the Eplore It mode for the followig eercise.. Move the slider bar as directed: orage) to - red) to a. Use the above eample i the Eplore It mode to complete the followig: Epoetial form Epaded form ) - ) - ) Juior High Math Iteractives Page 0 of 006 Alberta Educatio

11 b. Complete all the missig parts i the followig table: ) - Epoetial form Epaded form e.g. ) - )) ) ) ))) ) c. Complete the Negative Epoet Law: ) - is defied to be the reciprocal of ). 6 6 Juior High Math Iteractives Page of 006 Alberta Educatio