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# Exponents

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### Exponents

1. 1. Exponents Chapter 2 Lesson 2.8
2. 2. How does a secret spread so fast? <ul><li>The person with a secret tells a friend. </li></ul><ul><li>The friend promises never to tell anyone. </li></ul><ul><li>That same friend breaks the promise and tells two more friends. </li></ul><ul><li>The two new friends tell two new friends. </li></ul><ul><li>The two new friends decide to tell two more friends. </li></ul><ul><li>This pattern occurs over and over until many people have been told. </li></ul><ul><li>By the end of the day it is no longer a secret! </li></ul>
3. 3. Here is how a secret can spread. (Real Fast!) <ul><li>Round 1 Round 2 </li></ul>I have a secret and I tell 3 of my best friends. My 3 friends each tell 3 more people. Look how many people now know the secret! 3 x 3 = 9 9 people know!
4. 4. In an exponential expression, the base is the factor, and the exponent tells the amount of times to multiple that number by itself. (That is a mouthful!) <ul><li>3 </li></ul>4 Your BASE = 3 Your EXPONENT = 4 A base is a number that can be expressed using an exponent. An exponent is the small number and is referred to as a “power.” 3 4 means 3 x 3 x 3 x 3 OR 3 to the forth power.
5. 5. There are 3 ways to write an exponent. <ul><li>2 </li></ul>4 Factored Form is one way. In factored form you spread the equation apart – piece by piece to show what it means. 2 4 Means 2 x 2 x 2 x 2 This is factored form!
6. 6. Here is another way! <ul><li>Write a set of numbers as an exponent </li></ul><ul><li>x 2 x 2 x 2 = </li></ul><ul><li>List the base first = 2 </li></ul><ul><li>Then count up the number of two’s you see. There are 4 number 2’s. </li></ul><ul><li>Therefore 2 x 2 x 2 x 2 = </li></ul>2 4
7. 7. Here is the last way! (The Most Important Way) <ul><li>Standard Form is the easiest to write. </li></ul><ul><li>To write an exponent in standard form – JUST MULTIPLY! </li></ul>2 4 = 2 x 2 x 2 x 2 Now solve! 2 x 2 = 4 x 2 = 8 x 2 = 16
8. 8. Try This! <ul><li>3 5 – Write in factored form. </li></ul><ul><li>4 x 4 x 4 </li></ul><ul><li>Write as an exponent. </li></ul><ul><li>2 6 – Write in standard form. </li></ul><ul><li>3 x 3 x 3 x 3 x 3 </li></ul><ul><li>4 3 </li></ul><ul><li>2 x 2 x 2 x 2 x 2 x 2 = 64 </li></ul>
9. 9. Exponents in Shape Form <ul><li>Write the factored shape in exponent form. </li></ul>X X =