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Exponents Multiplying Monomials
What is does an exponent look like? <ul><li>It looks like a little number to the upper right of another one… </li></ul><ul...
What 3 2  means. <ul><li>Three times itself twice. </li></ul><ul><li>In numbers it means: 3 x 3. </li></ul>
What it does  NOT  mean <ul><li>3 2  does NOT mean 3x2. </li></ul><ul><li>This is a common mistake that students make. </l...
Let’s take a  at some number sentences that are equal to bases and exponents.
What does  4 2   mean? 4 2  = 4*4
4 3  means… 4 3  = 4*4*4
More powers of 4. <ul><li>4 4  = </li></ul><ul><li>4*4*4*4 </li></ul><ul><li>4 5  =  </li></ul><ul><li>4*4*4*4*4 </li></ul>
Powers of 10 <ul><li>10 2  = 10*10 =  </li></ul><ul><li>100 </li></ul><ul><li>10 3  = 10*10*10 = </li></ul><ul><li>1000 </...
What about a number to the first power? <ul><li>If 3 2  is 3*3, 3 1  is just one 3 </li></ul><ul><li>4 1  = 4 </li></ul><u...
Evaluate 6 3 <ul><li>E valu at e  means find the value </li></ul>
6 3  = (6x6)*6 <ul><li>(36)*6 = 216 </li></ul>
Assign 19-29; 35-49 odds <ul><li>#19 </li></ul><ul><ul><li>2 6  = </li></ul></ul><ul><ul><li>(2*2)*(2*2)*(2*2)= </li></ul>...
Product of Powers There’s a quick way to multiply numbers in exponential form.
Let’s look at numbers with the same base that have exponents. <ul><li>3 2  x 3 3  = (3*3)*(3*3*3) </li></ul><ul><li>How ma...
Let’s check that out. <ul><li>If 4 3  * 4 5  = (4*4*4)*(4*4*4*4*4) and </li></ul><ul><li>(4*4*4)*(4*4*4*4*4) = 4 8  then w...
Give your answers in exponential form. <ul><li>2 3 *2 4 </li></ul><ul><li>8 * 8 3 </li></ul><ul><li>y 2  * y 3 </li></ul><...
Answers in exponential form <ul><li>2 3 *2 4 =  2*2*2*2*2*2*2=2 7 </li></ul><ul><li>8 * 8 3 =8*(8*8*8)=8 4 </li></ul><ul><...
Multiplication of Monomials
What is a monomial? <ul><li>A monomial is an algebraic expression that is either a… </li></ul><ul><ul><li>Constant </li></...
Examples of monomials <ul><li>A monomial is an algebraic expression that is either a… </li></ul><ul><ul><li>Constant – 4  ...
Multiplication of Monomials <ul><li>Use the commutative and associative properties of multiplication to your advantage. </...
Let’s simplify 4a 2 b * 3 ab 3 <ul><li>4a 2 b * 3 ab 3   </li></ul><ul><li>= 4*a*a*b*3*a*b*b*b </li></ul><ul><li>=4*3*a*a*...
Try some <ul><li>(5t)(20t 3 )= </li></ul><ul><li>(4m 2 )(-16mn 2 )= </li></ul><ul><li>Answers on the next slide… </li></ul>
Answers <ul><li>(5t)(20t 3 )=5*t*20*t*t*t =5*20*t*t*t*t=100t 4 </li></ul><ul><li>(4m 2 )(-16mn 2 )=4*m*m*(-16)*m*n*n= </li...
 
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8 1 Exponents

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Transcript of "8 1 Exponents"

  1. 1. Exponents Multiplying Monomials
  2. 2. What is does an exponent look like? <ul><li>It looks like a little number to the upper right of another one… </li></ul><ul><li>Like this: 3 2 </li></ul><ul><li>In the number above, the 3 is called the base . The two is the exponent . </li></ul>
  3. 3. What 3 2 means. <ul><li>Three times itself twice. </li></ul><ul><li>In numbers it means: 3 x 3. </li></ul>
  4. 4. What it does NOT mean <ul><li>3 2 does NOT mean 3x2. </li></ul><ul><li>This is a common mistake that students make. </li></ul><ul><li>3 3 does not mean 6. </li></ul><ul><li>Students make the mistake of sometimes adding the base to the exponent. </li></ul>
  5. 5. Let’s take a at some number sentences that are equal to bases and exponents.
  6. 6. What does 4 2 mean? 4 2 = 4*4
  7. 7. 4 3 means… 4 3 = 4*4*4
  8. 8. More powers of 4. <ul><li>4 4 = </li></ul><ul><li>4*4*4*4 </li></ul><ul><li>4 5 = </li></ul><ul><li>4*4*4*4*4 </li></ul>
  9. 9. Powers of 10 <ul><li>10 2 = 10*10 = </li></ul><ul><li>100 </li></ul><ul><li>10 3 = 10*10*10 = </li></ul><ul><li>1000 </li></ul><ul><li>10 4 = 10*10*10*10 = </li></ul><ul><li>10,000 </li></ul>
  10. 10. What about a number to the first power? <ul><li>If 3 2 is 3*3, 3 1 is just one 3 </li></ul><ul><li>4 1 = 4 </li></ul><ul><li>5 1 = </li></ul><ul><li>5 </li></ul><ul><li>5 1 does NOT mean 5x1, it is five to the first power. </li></ul>
  11. 11. Evaluate 6 3 <ul><li>E valu at e means find the value </li></ul>
  12. 12. 6 3 = (6x6)*6 <ul><li>(36)*6 = 216 </li></ul>
  13. 13. Assign 19-29; 35-49 odds <ul><li>#19 </li></ul><ul><ul><li>2 6 = </li></ul></ul><ul><ul><li>(2*2)*(2*2)*(2*2)= </li></ul></ul><ul><ul><li>4*4*4 = 16*4 = </li></ul></ul><ul><li>#21 </li></ul><ul><ul><li>5 3 = 5*5*5= </li></ul></ul><ul><ul><li>25*5 = </li></ul></ul>
  14. 14. Product of Powers There’s a quick way to multiply numbers in exponential form.
  15. 15. Let’s look at numbers with the same base that have exponents. <ul><li>3 2 x 3 3 = (3*3)*(3*3*3) </li></ul><ul><li>How many threes are there? </li></ul><ul><li>How does five threes relate to the two exponents : 2 and 3? </li></ul><ul><li>3 2 x 3 3 = 3*3*3*3*3 = 3 5 </li></ul>
  16. 16. Let’s check that out. <ul><li>If 4 3 * 4 5 = (4*4*4)*(4*4*4*4*4) and </li></ul><ul><li>(4*4*4)*(4*4*4*4*4) = 4 8 then we should be able to add the exponents together. </li></ul><ul><li>9 2 *9 1 = 9 3 </li></ul><ul><li>(9*9)*9 = 81*9 = 729 </li></ul>
  17. 17. Give your answers in exponential form. <ul><li>2 3 *2 4 </li></ul><ul><li>8 * 8 3 </li></ul><ul><li>y 2 * y 3 </li></ul><ul><li>3 5 *3 3 </li></ul><ul><li>Click on the next slide when you are ready for the answers. </li></ul>
  18. 18. Answers in exponential form <ul><li>2 3 *2 4 = 2*2*2*2*2*2*2=2 7 </li></ul><ul><li>8 * 8 3 =8*(8*8*8)=8 4 </li></ul><ul><li>y 2 * y 3 =(y*y)*(y*y*y) = y 5 </li></ul><ul><li>3 5 *3 3 = 3*3*3*3*3*3*3*3 = 3 8 </li></ul><ul><li>Click on the next slide when you are ready for the answers. </li></ul>
  19. 19. Multiplication of Monomials
  20. 20. What is a monomial? <ul><li>A monomial is an algebraic expression that is either a… </li></ul><ul><ul><li>Constant </li></ul></ul><ul><ul><li>Variable, or </li></ul></ul><ul><ul><li>A product of a constant and one or more variables. </li></ul></ul>
  21. 21. Examples of monomials <ul><li>A monomial is an algebraic expression that is either a… </li></ul><ul><ul><li>Constant – 4 18 32 2 </li></ul></ul><ul><ul><li>Variable – x y m n </li></ul></ul><ul><ul><li>A product of a constant and one or more variables. 4xy 3mn 3n 8x 12y </li></ul></ul>
  22. 22. Multiplication of Monomials <ul><li>Use the commutative and associative properties of multiplication to your advantage. </li></ul><ul><li>Oftentimes it works well to separate your coefficients and variables, such as.. </li></ul>
  23. 23. Let’s simplify 4a 2 b * 3 ab 3 <ul><li>4a 2 b * 3 ab 3 </li></ul><ul><li>= 4*a*a*b*3*a*b*b*b </li></ul><ul><li>=4*3*a*a*a*b*b*b*b </li></ul><ul><li>= 12a 3 b 4 </li></ul>
  24. 24. Try some <ul><li>(5t)(20t 3 )= </li></ul><ul><li>(4m 2 )(-16mn 2 )= </li></ul><ul><li>Answers on the next slide… </li></ul>
  25. 25. Answers <ul><li>(5t)(20t 3 )=5*t*20*t*t*t =5*20*t*t*t*t=100t 4 </li></ul><ul><li>(4m 2 )(-16mn 2 )=4*m*m*(-16)*m*n*n= </li></ul><ul><li> 4*(-16)*m*m*m*n*n= </li></ul><ul><li>-64m 3 n 2 </li></ul>
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