Exponents

How can I write 2 + 2 + 2 + 2 using multiplication? Prior Knowledge Years ago you learned that multiplication is an easier way to show repeated addition. Example: How can I write 2 + 2 + 2 + 2 using multiplication? 2 x 4

How can I write 2 x 2 x 2 x 2 using exponents? Exponential Form Writing numbers in exponential form is just an easier way to show repeated multiplication. Example: How can I write 2 x 2 x 2 x 2 using exponents? 2 x 2 x 2 x 2 = How many twos are shown? 24 1 2 3 4

32 means 3 is multiplied by itself 2 times Vocabulary baseexponent An exponent tells how many times a number (called the base) is multiplied by itself. exponent 3² base 32 means 3 is multiplied by itself 2 times

4 is multiplied by itself 3 times So… 43 4 is multiplied by itself 3 times 43 = 4 x 4 x 4 = 64 43 ≠ 4 x 3

There are two specially-named powers: Reading Exponents 46 is read “4 to the sixth power.” 51 is read “5 to the first power.” 38 is read “3 to the eighth power.” And so on… There are two specially-named powers: 32 is read “3 to the second power” or “3 squared.” 43 is read “4 to the third power” or “4 cubed.”

Write each in exponential form and find the value. 2 x 2 x 2 x 2 7 x 7 1 x 1 x 1 x 1 5 x 5 x 5 6 24 = 16 72 = 49 14 = 1 53 = 125

Write each as repeated multiplication and find the value. 32 33 101 25 3 x 3 = 9 3 x 3 x 3 = 27 10 2 x 2 x 2 x 2 x 2 = 32

What about a number raised to the power of ZERO? Example: What is 30 ? Complete the table below. See if YOU and your partner can see the pattern to figure it out…. 34 3x3x3x3 = 81 33 32 31 30

What about a number raised to the power of ZERO? Example: What is 30 ? Did you find that dividing by 3 gives you the next value? 34 3x3x3x3= 81 33 3x3x3 =27 32 3x3 =9 31 3 30 1

What about a number raised to the power of ZERO? FACT: All positive numbers raised to the power of zero are equal to 1. 20 = 1 40 = 1 1,000,0000 = 1