CONFIDENTIAL1 Warm-up:1.) 2 x 2 x 2 = 2.) 5 x 5 = 3.) 4 x 4 x 4 = 4.)10 x 10 x 10 x =

CONFIDENTIAL2 Remember that any number can be written as a product of Prime Factors. Example: The Number 32 can be written as 2 x 2 x 2 x 2 x 2

CONFIDENTIAL3 Example: The Number 32 can be written as 2 x 2 x 2 x 2 x 2 A product of prime numbers can be expressed using EXPONENTS and a BASE 2525

CONFIDENTIAL4 Numbers expressed using Exponents are called Powers WordsExpressionsValue to the fifth power 3 to the second power or 3 squared 10 to the third power or 10 cubed 2 x 2 x 2 x 2 x 2 3 x 3 10 x 10 x ,000

CONFIDENTIAL5 There are several symbols you might see for Multiplication 2 x 2 x 2 = * 2 * 2 = = 2 3..

CONFIDENTIAL6 Let's Practice... If we write 3 x 3 x 3 x 3 using an exponent, the base is 3 AND the exponent is = 3 4 = 81...

CONFIDENTIAL7 We can also refer to writing 4 5 as a PRODUCT OF THE SAME FACTOR (Remember that a "Product" is the answer to a multiplication problem.) The Base is 4. The Exponent is 5. So 4 is a Factor 5 times. 4 5 = 4 x 4 x 4 x 4 x 4 = 1,024

CONFIDENTIAL8 Your Turn! Write 7 x 7 x 7 using an Exponent. Then find its value.

CONFIDENTIAL9 Write 2 3 as a product of the same factor. Then find its value.

CONFIDENTIAL10 Exponents can be used to write the Prime Factorization of a number. Example: x x xx x x OR 2 3 x 3 (Start with the smallest prime factor)

CONFIDENTIAL11 Your Turn! Write the Prime Factorization of the number using Exponents. 90

CONFIDENTIAL12 Your Turn! Write the Prime Factorization of the number using Exponents. 120

CONFIDENTIAL13 Any number to the 1 power equals itself. Example: 10 1 = = 5 2,345 1 = 2,345 Any number to the 0 power equals 1. Example:10 0 = = 1 2,345 0 = 1

CONFIDENTIAL14 Practice Problems: Write each product using an exponent. Then find its value. 1.) 2 x 2 x 2 x 2 = 2.) 6 x 6 x 6 = Write each power as a product of the same factor. Then find its value. 3.)2 6 = 4.)3 4 = Write the prime factorization of this number using exponents. 5.) 48

CONFIDENTIAL15 6.) Find the value of ) Find the value of 236 0

CONFIDENTIAL16 Write the values for these powers of 10. a) 10 1 = b) 10 2 = c) 10 3 = d) 10 4 = e) 10 5 = f) Describe the pattern for the powers of 10.

CONFIDENTIAL17 An estimated 10 9 people in the world speak Mandarin Chinese. About how many people speak this language?

CONFIDENTIAL18 1. Can you write this product using an exponent? 6 x 6 x 6 x 6 2. Can you find the value of this product? 5 x 5 x 5 3. Can you write this power as a product of the same factor? Can you find the value of this power? 2 4 Let's see how well we know Powers and Exponents!

CONFIDENTIAL19 6. Find the prime factorization of this number using exponents Can you find the value of this power? 57 0

CONFIDENTIAL20 Well Done!! We learned that POWERS are numbers expressed using exponents. 3 4 We learned that a product of prime factors can be written using a Base and Exponents. 2 3 = 2 x 2 x 2 = 8 We learned how to find the value of x 4 x 4 = 64 We learned how to write the Prime Factorization of a number using exponents. 24 = 2 x 2 x 2 x 3 = 2 3 x 3