Exponent Power Point


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powerpoint showing use of exponents

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Exponent Power Point

  1. 1. Can You Think Exponentially?
  2. 2. Changes, Changes, Changes <ul><li>What types of new technologies exist today that didn’t exist when I was your age? </li></ul><ul><li>Video </li></ul>
  3. 3. In Other Words… <ul><li>The world is changing exponentially! </li></ul><ul><li>As a result, we have to find a way to show very large numbers in a much easier way. </li></ul><ul><li>In other words, it would take quite a long time to write: </li></ul><ul><li>2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 </li></ul><ul><li>WOW! </li></ul><ul><li>Can’t there be a better way? </li></ul>
  4. 4. Yes – There is a Better Way! <ul><li>Exponents are a shorthand way to show how many times a number, called the base , is multiplied times itself. </li></ul><ul><li>Exponents look like this: 2 ³ </li></ul><ul><li>It would be: 2 x 2 x 2 </li></ul><ul><li>The number 2 is the base. The 3 is the exponent. </li></ul><ul><li>A number with an exponent is said to be &quot;raised to the power&quot; of that exponent. </li></ul>
  5. 5. Here are some simple rules to use with exponents. <ul><li>a1 = a </li></ul><ul><li>Any number raised to the power of one equals the number itself. </li></ul><ul><li>For any number a, except 0, a0 = 1 Any number raised to the power of zero, except zero, equals one. </li></ul><ul><li>For any numbers a, b, and c, ab x ac = ab+c This multiplication rule tells us that we can simply add the exponents when multiplying two powers with the same base. </li></ul>
  6. 6. ALERT! These are mistakes that students often make when dealing with exponents. <ul><li>Mistake! Do not multiply the base and the exponent. 26 is not equal to 12, it's 64! </li></ul><ul><li>Mistake! The multiplication rule only applies to expressions with the same base. Four squared times two cubed is not the same as 8 raised to the power two plus three. </li></ul><ul><li>Mistake! The multiplication rule applies just to the product, not to the sum of two numbers. </li></ul>
  7. 7. Let’s Take a Look at Some Examples <ul><li>Examples </li></ul><ul><li>At home, if you want to try more, here is another place to practice . </li></ul>
  8. 8. Here’s a problem for you to solve: <ul><li>If a school can hold 1,200 students, how many days would it take to fill the school if you started with 2 students and increased exponentially by 3 each day? </li></ul><ul><li>Answer: 2³ = 2x2x2 = 8 – Day 1 </li></ul><ul><li>8³ = 8x8x8 = 512 – Day 2 </li></ul><ul><li>512³ = 512x512x512 = 134,217,728 – Wow – That school Is already overcrowded by day 3! </li></ul><ul><li>This demonstrates to students how things can increase so much faster exponentially. </li></ul>