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Lesson Objective: I can… Understand that 3x = x + x + x is not the same thing at x 3. Understand that a base number can be represented with a positive whole number, positive fraction, or positive decimal and that for an number, a, we define a m to be the product of m factors and a.

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Evaluate these expressions, pay attention as to how you arrived at your answers. 4+4+4+4+4+4+4+4+4+4 9+9+9+9+9 10+10+10+10+10

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1. How many of you solved the problem by “counting on”? 2. How else could you have solved this problem?

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The little number in exponents is known as a subscript. 10 5 Why is it important that we write exponents carefully?

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Write each expression in exponential form. 1. 5×5×5×5×5= 2. 2×2×2×2= Write each expression in expanded form. 3. 83= 4. 106= 5. 3=

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What is the difference between 3g and g 3 ?

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6. Write the expression in expanded form, and then evaluate. (3.8)4= 7. Write the expression in exponential form, and then evaluate. 2.1×2.1= 8. Write the expression in exponential form, and then evaluate. 0.75×0.75×0.75= The base number can also be a fraction. Convert the decimals to fractions in Examples 7 and 8 and evaluate. Leave your answer as a fraction. Remember how to multiply fractions!

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9. Write the expression in exponential form, and then evaluate. 1/2×1/2×1/2= 10. Write the expression in expanded form, and then evaluate. (2/3) 2 =

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Fill in the chart, supplying the missing expression. 1. Fill in the missing expression for each row. For whole number and decimal bases, use a calculator to find the standard form of the number. For fraction bases, leave your answer as a fraction. Exponential Form Expanded FormStandard Form 3232 3 x 39 2 x 2 x 2 x 2 x 2 x 2 4545 ¾ x ¾ 1.5 x 1.5

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2. Write five cubed in all three forms: exponential form, expanded form, and standard form. 3. Write fourteen and seven-tenths squared in all three forms. 4. One student thought two to the third power was equal to six. What mistake do you think he made, and how would you help him fix his mistake?

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EXPONENTIAL NOTATION FOR WHOLE NUMBER EXPONENTS: Let be a nonzero whole number. For any number, the expression m is the product of factors of. The number is called the base, and is called the exponent or power of. When is 1, “the product of one factor of ” just means, i.e., 1 =. Raising any nonzero number to the power of 0 is defined to be 1, i.e., 0 =1 for all ≠0.

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Scientific notation is a way of expressing really big numbers or really small numbers. It is most often used in “scientific” calculations where the.

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