As I was going to St. Ives I met a man with seven wives,  Each wife had seven sacks, each sack had seven cats,  Each cat had seven kits: kits, cats, sacks and wives,  How many were going to St. Ives? 

3 2 3 2

3 3

3

Exponents

Exponent Base Number 3 2 This is read as, “2 to the third power.” How many times the base number is multiplied by itself 2 Base Number The number being multiplied over and over again This is read as, “2 to the third power.” This expression is saying 2 times itself 3 times. 2 ● 2 ● 2

How Do You Read… 42 = 83 = 25 = 4 to the second power 8 to the third power 2 to the fifth power

There are fancy ways to read exponents of two and three… do you know what they are and why we use these fancy words? Any base number to the power of 2 is read as, “a number squared” ex: 92 is read, “nine squared.” Any base number to the power of 3 is read as, “a number cubed” ex: 93 is read, “nine cubed.”

Expanded Notation 56 38 99 5 ● 5 ● 5 ● 5 ● 5 When an a number in exponential notation is written as an expression using repeated multiplication it is known as standard or expanded notation. Exponential Notation Expanded Notation 56   38 99 5 ● 5 ● 5 ● 5 ● 5 3 ● 3 ● 3 ● 3 ● 3 ● 3 ● 3 ● 3 9 ● 9 ● 9 ● 9 ● 9 ● 9 ● 9 ● 9 ● 9

Let’s Try a Few… 42 = 4 ● 4 = 16 83 = 8 ● 8 ● 8 = 512 25 = 2 ● 2 ● 2 ● 2 ● 2 = 32

= < < Exponent Battle 42 vs. 24 83 vs. 38 25 vs. 63 Use >, < or = to determine who wins the battle. 42 vs. 24 83 vs. 38 25 vs. 63 = < <

Extension – Zero Power 21 = 22 = 23 = 24 = 25 = What do you think the value of 30 is? Let’s see if we can find a pattern that will help us determine the answer using a different number such as 20... 21 = 22 = 23 = 24 = 25 = Will this pattern work for any base number to the power of zero ? As we work our way through the next exponent up we simply multiply the previous answer by the base number. If we wanted to work backwards we would use the opposite of multiplication which is division.

Extension – Square Roots  

Extension – Square Roots