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Exponents. 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. Exponent How many times the base number is multiplied by itself. 2.
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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 Exponent 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… 4 to the second power 42 = 83 = 25 = 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.”
3 2 3 2
3 3
3 3 3
Let’s Try a Few… 42 = 4 ● 4= 16 83 =8 ● 8 ● 8= 512 25 = 2 ● 2● 2● 2● 2= 32
Exponent Battle Use >, < or = to determine who wins the battle. 42 vs. 24 83 vs. 38 25 vs. 63 = < <
Extension – Zero Power • 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 • The opposite of addition is subtraction • The opposite of multiplication is division • The opposite of an exponent is its square root • The symbol we use for a square root is _____. It is called the radicalsymbol • For example we would read _____ as “radical 9.” • When you see a number under the radical symbol it simply ask yourself, “what number times itself is equal to that number?” • Not every number will have a perfect square root. A perfect square root occurs only when you have an answer that is a whole number.
Extension • The opposite of addition is subtraction • The opposite of multiplication is division • The opposite of an exponent is its square root • The symbol we use for a square root is _____. It is called the radicalsymbol • For example we would read _____ as “radical 9.” • When you see a number under the radical symbol it simply ask yourself, “what number times itself is equal to that number?” • Not every number will have a perfect square root. A perfect square root occurs only when you have an answer that is a whole number.
Extension – Square Roots How do you read ? Write your answer two different ways. 1)__________________________________________________ 2)__________________________________________________ What is the solution to the previous radical? _________ How do you read ? Write your answer two different ways. 1)__________________________________________________ 2)__________________________________________________ What is the solution to the previous radical? _________ How do you read ? Write your answer two different ways. 1)__________________________________________________ 2)__________________________________________________ What is the solution to the previous radical? _________ The square root of 25 Radical 25 5 The square root of 81 Radical 81 9 The square root of 75 Radical 75 Not a perfect square
