Lesson: 8.EE.A.1 Part 1 - currituck.k12.nc.us



Lesson: 8.EE.A.1 Part 1Part 1: Product Rule of ExponentsWithout a calculator, expand the expression and find the value:24 ? 23= 32 ? 33=55 ? 54= What pattern do you notice?Product Rule: for any nonzero rational number a and integers n and m, an ? am= Which expression is equivalent to 24 ? 242162848416Which expression is equivalent to -53 ? -55-58-5152582515-2515Which expression is equivalent to 352 ? 35392569255356355Which expression is equivalent to -342 ? -344-3469168-9166-9168Which expression is equivalent to 42 ? 43 ? 44642464949424James wrote the following equation: 34 ? 9= 36Using properties of exponents, explain why he is correct.Part II:Without a calculator, expand the expression and find the value:232=333= 254= What pattern do you notice?How is this pattern related to the rule from Part I?Rule: for any nonzero rational number a and integers n and m, anm = Which expression is equivalent to 43346243649What value of n would make the equation true?2n2=28What value of n would make the equation true?43 ? 42n= 415Which expression is equivalent to 2?23245462826Select all expressions equivalent to 43?424412 ? 4845 ? 4445 ? 45 ? 45 ? 45464Select all expressions equivalent to -34?-332-39-314-38?-36-36?-35-324Part III: Quotient Rule of ExponentsIn Part I, you discovered 24 ? 23= 27Because 24 ? 23= 27 could be expanded to 2?2?2?2?2?2?2= 27Using your work in Part I and Part II, expand the following numerical expressions.24 ÷ 23=36 ÷ 34= 55 ÷ 52= What pattern do you notice?Quotient Rule: for any nonzero rational numbers a and integers n and m, am÷an=Which expression is equivalent to 3431?33413-3What value of n will make the equation true?45÷43n= 44Select all expressions equivalent to 23?2425242222212254725Which expression is equivalent to 33?3291943339Part IV: Negative and Zero ExponentsIn Part III above, you discovered the property of division of expressions with integer exponents. Use that work to determine what happens when the exponent of the number in the denominator is greater than the exponent of the number in the numerator:Instead of using the property, we could rewrite it in the expanded form53 ÷ 55=Thus, 5-2= 25 ÷ 28= Thus, 2-3=What pattern do you notice?Task:In this problem?c?represents a positive number.?The quotient rule for exponents says that if?m?and?n?are positive integers with?m>n, thencmcn=cm-nUsing the quotient rule and the work you did above, complete the following exploration of the quotient rule when?m≤n:What expression does the quotient rule provide for?cmcn when?m=n?If?m=n, simplify?cmcn?without using the quotient rule.What do parts (a) and (b) above suggest is a good definition for?c0?What expression does the quotient rule provide for?c0cn?What expression do we get for?c0cn??if we use the value for?c0?found in part (c)?Using parts (d) and (e), propose a definition for the expression?c-n.Negative Exponent Rule: For any nonzero rational number a and integer n, a-n= Zero Exponent Rule: For any nonzero rational number a, a0= Select all expressions equivalent to 43?424412 ? 4845 ? 4445 ? 45 ? 45 ? 45464Select all expressions equivalent to -34?-332-39-314-38?-36-36?-35-324Which expression is equivalent to 3431?33413-3What value of n will make the equation true?45÷43n= 44Select all expressions equivalent to 23?2425242222212254725Select all expressions equivalent to 45?4-3-212562564-10?4643?4-5Select all expressions equivalent to 1262-5?· 2-12-3?· 222-2?· 2-421?· 2521?· 2622?· 2-823?· 23Select all expressions equivalent to 3-83-43-123-4321321341312Show that 353-7= 312Show that 2-2-3=26What is 200?What is 10? ................
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