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Dealing with Exponents

Dealing with Exponents. What do exponents mean . What does 4 2 ? To multiply 4 by itself 2 times 4 x 4 Well what about 4 -2 ? or 4 5 x 4 2 ?. Dealin with inverses Example: 4 -2. A number or letter raised to a negative power means to flip and simplify Ex. 3 -2 = a -3 =

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Dealing with Exponents

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  1. Dealing with Exponents

  2. What do exponents mean • What does 42 ? • To multiply 4 by itself 2 times • 4 x 4 • Well what about 4-2? or 45 x 42?

  3. Dealin with inverses Example: 4-2 • A number or letter raised to a negative power means to flip and simplify • Ex. 3-2= a-3= • = 53 = y 1 1 a3 32 1 1 y-1 5-3

  4. 2. 7–2 3. (–2)–5 1 – = 1 = 32 49 for Examples 3 and 4 GUIDED PRACTICE

  5. When we have the same numbers or letters being multiplied or divided with different exponents we do something different Multiplication we add the exponents ex. 22 • 24 = 22+4 = 26

  6. Simplifyx4x7. x4x7 = x4 +7 EXAMPLE 1 Using the Product of Powers Property Product of powers property = x11 Add exponents.

  7. 3. a6a9 4. cc12 c3 for Examples 1 GUIDED PRACTICE Simplify the expression. Write your answer as a power. = a15 = c16

  8. 1. 46 44 2. 98 9 for Examples 1 GUIDED PRACTICE Simplify the expression. Write your answer as a power. = 410 = 99

  9. Simplify32x2 3x3. 32x2 3x3 = (32 3) (x2x3) = 32+1x2+3 EXAMPLE 2 Using the Product of Powers Property Use properties of multiplication. Product of powers property = 33x5 Add exponents. = 27x5 Evaluate the power.

  10. 5. 102s4 104s2 for Examples 2 GUIDED PRACTICE Simplify the expression. = 1,000,000 s6

  11. 6. 63t5 62t8 for Examples 2 GUIDED PRACTICE Simplify the expression. = 7776 t13

  12. 7. 7x2 7x4 for Examples 2 GUIDED PRACTICE Simplify the expression. = 49 x6

  13. 8. 52z 5z7z2 for Examples 2 GUIDED PRACTICE Simplify the expression. = 125 z10

  14. Simplify 16.   (10v5)(-7v6u2)17.   (-10e4)(2e5)18.   (3i2)(-9i6n2)(-4i6n4)19.   (-4m3)(-m2)(7m5v4)20.   (9z4)(-8z2)21.   (-8a4g6)(4a5)(-9a4)22.   (-4t3g6)(-12t2g5)23.   (9n5)(-n2g6)24.   (-10m6)(-9m2)(12m2r5)25.   (11a5)(-12a3e5)26.   (10h2)(-5h5)27.   (-2t2y3)(9t3y3)(-6t3)28.   (-4w6)(-w2s3)29.   (8d6)(-6d2b5)30.   (10s4e5)(3s2e5) • 1.   (-11m4)(-6m3p2)2.   (-2f3)(-3f4s3)3.   (10v2)(v2k6)4.   (-5l6h4)(10l6h6)5.   (-5f2)(f3c3)6.   (-12b3z4)(-11b5z5)7.   (7w6m2)(9w3m3)8.   (-6t5)(-5t6x3)9.   (4r5e4)(3r4)10.   (2g3)(-3g6u6)11.   (-11s4)(-5s3f2)(-2s6)12.   (-5o3)(3o6)(-7o2)13.   (p6)(8p5n4)14.   (-6t4i5)(-10t4)15.   (-8b2)(-b6q3)

  15. Dividing Exponents • When we have division we subtract the two exponents from themselves. • Subtract from the higher number where its at. ex. x7 j2 1 = = x7-4 x4 j5 j5-2 = x3 1 = j3

  16. Examples 1 23 = 3x7 3x7-4 = 25 25-3 9 9x4 1 = 22 x3 = 3 1 = 4

  17. Simplify • 1.   (7)2   ÷   74 • 2.   92   ÷   9-3 • 3.   (3)4   ÷   39 • 4.   58 ÷ 55 • 5. x-3 • x5 • 6. 29 • 2-11

  18. Homework

  19. Scientific Notation • Is taking a large number and making it to into a more reasonable number. • Ex. 14500000000000 → 1.45 x 1013 • The Only Rule is the Base number has to be between 1 and 10

  20. Stars There are over 300,000,000,000 stars in the Andromeda Galaxy. Write the number of stars in scientific notation. Standard form Product form Scientific notation 300,000,000,000 3 100,000,000,000 3 1011 ANSWER The number in scientific notation is 3 1011. EXAMPLE 1 Writing Numbers in Scientific Notation SOLUTION Move decimal point 11 places to the left. Exponent is 11.

  21. Standard form Scientific notation Product form 4000 4 1000 4 103 for Example 1 GUIDED PRACTICE Write the number in scientific notation. 1.4000 SOLUTION

  22. Standard form Scientific notation Product form 7,300,000 7.3 1,000,000 7.3 106 for Example 1 GUIDED PRACTICE 2. 7,300,000 SOLUTION

  23. Standard form Scientific notation Product form 63,000,000,000 6.3 10,000,000,000 6.3 1010 for Example 1 GUIDED PRACTICE 3. 63,000,000,000 SOLUTION

  24. Standard form Scientific notation Product form 230,000 2.3 100,000 2.3 105 for Example 1 GUIDED PRACTICE 4. 230,000 SOLUTION

  25. Standard form Scientific notation Product form 2,420,000 2.42 1,000,000 2.42 106 for Example 1 GUIDED PRACTICE 5. 2,420,000 SOLUTION

  26. Standard form Scientific notation Product form 105 1.05 100 1.05 102 for Example 1 GUIDED PRACTICE 6. 105 SOLUTION

  27. Example 2 • Given: 0.000567 • Use: 5.67 (moved 4 places) • Answer: 5.67 x 10-4

  28. Why did the last slide have the scientific notation to x 10-4 • What definition or rule we make about this

  29. Changing scientific notation to standard form.

  30. To change scientific notation to standard form… • Simply move the decimal point to the right for positive exponent 10. • Move the decimal point to the left for negative exponent 10. (Use zeros to fill in places.)

  31. Example 3 • Given: 5.093 x 106 • Answer: 5,093,000 (moved 6 places to the right)

  32. Example 4 • Given: 1.976 x 10-4 • Answer: 0.0001976 (moved 4 places to the left)

  33. When multiplying 2 or more scientific numbers we must still follow the rule of Scientific Notation making sure the base is still between 1 and 10 • Do the following

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