Exponents 𝑥 2 Powers and Exponents 6.1 p. 433

What is our goal? We will review the vocabulary associated with exponents and exponential notation We will extend this idea to evaluate exponents correctly with the order of operations

Vocabulary base Exponent (indicates power) The number used as a factor Exponent (indicates power) tells how many times a base is used as a factor exponential form 2 x 2 x 2 x 2 x 2 = 25 base This tells us to multiply 2 by itself five times.

10 x 10 = 102 10 9 Exponent Factors Base 2. In your notes, write your own example. In your own words, write the definition of an exponent. Compare it to that of another person in your group. Key words: base, multiplied, power MP3 players come in different storage sizes, such as 2GB, 4GB, or 16 GB, where GB means gigabyte. One gigabyte is equal to 10·10·10·10·10·10·10·10·10 bytes. In exponential notation, this would be 10 9

Write Products as Powers p. 434 100 is a perfect square. 10 x 10 x 10 = 1000 10 3 =1000 ** 3 1000 =10 radical sign 10 x 10 = 100 10 2 =100 ** 100 =10 radical sign Other perfect squares……..WHY?? 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169…… Perfect cubes are numbers with three identical whole number factors…..a number that has been “cubed” or multiplied by itself three times. Because 4 x 4 x 4 = 64, 64 is a perfect cube.

Examples 6 ∙ 6 · 6 ∙ 6 with an exponent Got it???? 74 97 1. Write 6 ∙ 6 · 6 ∙ 6 with an exponent It is often helpful to write what the exponential form means 6 x 6 x 6x 6 = 64 2. Write 4 x 4 x 4 using an exponent 4 3 The factor _____ is the base. The factor is multiplied (by itself) ______ times. The exponent is _____. The exponential form is _________ 43 Got it???? 7(7)7(7) = 74 9 x 9 x 9 x 9 x 9 x 9 x 9 = 97

Writing Powers as Products p. 435 Determine the base and the exponent. 102 10 is the base, 2 is the exponent. This would be read as “10 squared.” if it were 103 we would read this as “10 cubed.” 3. Write 52 as the product of the same factor. By writing what it means, you can keep track of how many times you have used the base. 52 = 5 x 5 = 25 4. Write 1.53 as the product of the same factor.  x 1.5 1.5 x 1.5 (1.5)(1.5)(1.5) = 2.25 1125 75 150 2250 2.25 3.375

5. Write 1 2 3 as the product of the same factor. 1 2 𝑥 1 2 𝑥 1 2 = 1 4 𝑥 1 2 = 1 8 WAIT!!!!! Got it???? (10)10(10)10(10) = 105 = 100,000 21 x 21 2.12 = 2.1 x 2.1 21 420 4.41 1 4 2 = 1 4 𝑥 1 4 = 1 16

There is a notation on the side of this page that talks about the exponent and the fraction. Right now, just remember that ANYTIME you have an exponent outside of a set of parentheses, the base is ALWAYS the value that is inside the ( ).

Guided Practice……p. 436 8 3 1 5 1. 8 x 8 x 8 = 2. 1 x 1 x 1 x 1 x 1= Write each power as a product, then find the value. (Expand and evaluate) 3. ( 1 7 ) 3 1 7 𝑥 1 7 𝑥 1 7 = 1 49 ∙ 1 7 = 1 343 4. 25 = 2 x 2 x 2 x 2 x 2 = = 4 x 4 x 2 = 16 x 2 = 32 14 x 14 5. 1.42 = 56 1.4 ( 1.4) = 140 1.96

≈343 𝑓𝑡. 6. Coal mines have shafts that can be as much as 7 3 feet deep. About how many feet deep into the Earth’s crust are these shafts? (Look back at your work!!) ≈343 𝑓𝑡. 7. How is using exponents helpful? Don’t forget to rate your understanding!!

What did we accomplish? Your homework will be additional practice on the lesson.