Exponents Grade 6+

​Exponents Grade 6+ Pt.1

8*9 we know mutliplication can be seen as repeated addition 8*9=8+8+8+8+8+8+8+8+8=72 but i want to introduce you to the new operation called exponets which can we used as repeated multiplication say we get 8⁹ denote it is repeated mutliplication we get 8⁹=8*8*8*8*8*8*8*8*8=134,217,728 lets try another one 2⁷=2*2*2*2*2*2*2=128 lets try last one 10¹⁰=10*10*10*10*10*10*10*10*10*10=10,000,000,000 now i want you to try thr try of the exersizes on your own and see how far you get

Multiple Choice

1. 1. 7¹

• 6

• 7

• 49

• 8

Multiple Choice

2. 2. 9³

• 6

• 12

• 27

• 729

Multiple Choice

3. 3. 3⁵

• 27

• 81

• 243

• 729

Multiple Choice

4. 4. 2⁸

• 256

• 0.25

• 16

• 64

Multiple Choice

5. 5. 6²

• 18

• 3

• 12

• 36

​we know that 7³=7*7*7=343 and 10⁷=10*10*10*10*10*10*10=10,000,000 but what if we have an negative power well we are going to use a formula if a^-n is the case than
a^-n=1/aⁿ say we got 8^-4=1/8⁴=1/4,096 we are going to try few examples say we have 7^-2=1/7²=1/49 and another one 10^-9=1/10⁹=1/1,000,000,000 and another one
5^-3=1/5³=1/125 and another one 2^-12=1/2¹²=1/4,096 what if we encounter 9⁰ note anything raised to the 0th power is 1 so 9⁰=1 always remember anything raised to 0 is 1 no debate on it now i want you to try the rest of the excerises on your own and see how far you get

​Exponents Grade 6+ Pt.2

Multiple Choice

6. 6. 9^-2

• 1

• -81

• ________

  .0123456789

• _______

  .012345679

Multiple Choice

7. 7. 10^-4

• .0001

• -10,000

• 100

• 10,000

Multiple Choice

8. 8. 3^-4

• _

  .2

• _______

  -.012345679

• -12

• _______

  .012345679

Multiple Choice

9. 9. 10⁰

• 10

• 1

• 0

• 100

Multiple Choice

10. CHALLANGE 10. ∞^-1

• 0

• 1

• -∞

• ∞

​Exponents Grade 6+ Pt.3

​say we get 2¹2³ you might say since were multiplying we should multiply the exponents but you are wrong we add then using the following rule aⁿa^m=a^n+m we can do the same with our problem heres the solution 2¹2³=2¹⁺³=2⁴=16 if you try using other method like 2¹2³=2¹*2³=2*8=16 you are going to get the same answer say i got another ploblem 3²3³ to solve that use aⁿa^m=a^n+m solve it while using a method formula 3²3³=3²⁺³=3⁵=243 lets try another method 3²3³=3²*3³=9*27=243 lets try another one 7¹7³ using the formula aⁿa^m=a^n+m to solve it so 7¹7³=7¹⁺³=7⁴=2,401 try another way 7¹7³=7¹*7³=7*343=2,401 lets the last one 6³6⁴ using the formula aⁿa^m=a^n+m to solve it so 6³6⁴=6³⁺⁴=6⁷=279,936 if you try another method we get 6³6⁴=6³*6⁴=216*1,296=279,936 now i want you to try the rest of the excerises on your own and see how far you get.

Multiple Choice

11. 11. 2^-32¹

• -,125

• ,25

• ,125

• -,25

Multiple Choice

12. 12. 5¹5^-2

• -.04

• .2

• -.2

• -04

Multiple Choice

13. 13. 4^-24¹

• .25

• -4

• -.0625

• .0625

Multiple Choice

14. 14. 4³4^-1

• -64

• .015625

• 16

• .0625

Multiple Choice

11. 15. 9⁴9^-2

• -43,046,721

• -531,441

• 81

• .00000002323

​Exponents Grade 6+ Pt.4

​say i got 7³/7² and i want to divide then you might think we can divivde the expoents but you are wrong we subtract them using this rule aⁿ/a^m=a^n-m we can apply the same method on the ploblem we got so 7³/7²=7^3-2=7¹=7 if you done a different method like this 7³/7²=343/49=7 you are going to get the same result lets try another one 4/4^-3 again use the dividing formula with exponents aⁿ/a^m=a^n-m so 4/4^-3=4¹/4^-3=4^1-(-3)=4¹⁺³=4⁴=256 lets try another one 8¹⁰⁰/8⁹⁷ again use the same dividing with exponents formula aⁿ/a^m=a^n-m lets apply the same interperatation 8¹⁰⁰/8⁹⁷=8^100-97=8³=512 you might try using a calculator but it isnt neccesary so always use the quick method we give you now i want you to try the rest of the excerises on your own and see how far you get

Multiple Choice

16. 16. 7²/7

• -7

• 49

• 7

• -49

Multiple Choice

17. 17. 7^-2/7^-5

• -3,647,327

• 343

• -343

• 3,647,327

Multiple Choice

18. 18. 7^2,203/7^2,200

• -343

• 343

• -∞

• ∞

Multiple Choice

19. 19. 10^10,000/10^9,990

• -10,000,000,000

• 10,000,000,000

• -∞

• ∞

Multiple Choice

20. CHALLANGE 20. (5⁷/5^-3)/(5³5⁴)

• ∞

• 125

• -125

• -∞

​Exponents Grade 6+ Pt.5

​say i got (5²)¹ and we need to do is to raise tihs exponent to the 1st power especially the exponent so what weuse is the base exponent by exponent rule we have (aⁿ)^m=a^nm we can use the same interperatation with our ploblem we have here so (5²)¹=5^2*1=5²=25 let's try another one say i got (4³)³ again use the formula (aⁿ)^m=a^nm so (4³)³=4^3*3=4⁹=262,144 lets try another one (7⁰)⁹⁴³ again use the formula (aⁿ)^m=a^nm so (7⁰)⁹⁴³=7^0*943=7⁰=1 lets try another one (4²³⁵)⁰ again use the formula (aⁿ)^m=a^nm so (4²³⁵)⁰=4^235*0=4⁰=1 lets try the last one (2⁴)^-3 again use the formula (aⁿ)^m=a^nm so (2⁴)^-3=2^4*-3=2^-12=1/2¹²=1/4,096=.000244140625 now i want you to try the rest of the excerises on your own and see how far you get

Multiple Choice

21. (3⁵)³/(3⁴)⁴

• _

  .3

• _

  -.3

• 3

• -3

Multiple Choice

22. 22. (2⁴)³(2⁶)^-2/(2²)²

• 1.25

• .0625

• .03125

• .015625

Multiple Choice

23. CHALLANGE 23. ((3²)⁴(3⁵)³)²/((3³)⁴(3²)²)³

• 2

• 9

• _

  .1

• -2

Multiple Choice

24. 24. (3³3^-2)⁴

• 27

• 81

• 243

• 729

Multiple Choice

25. CHALLANGE 25. (5^{7^2}/(5⁶)⁸)²

• 1

• 5

• 25

• 125

​Exponents Grade 6+ Pt.6

say i got an expression 8^8/3 and we want to evaluate it using some method so what we use a root law formula which is a^n/m=^m√aⁿ we can use the same interperatation so we get 8^8/3=³√8⁸=³√16,777,216=512 lets try another one 10^100/10 to solve it use the root formula 10^100/10=¹⁰√10¹⁰⁰=¹⁰√1e+100=10,000,000,000 lets try another one 2^10/5 to solve it use the root formula 2^10/5=⁵√2¹⁰=⁵√1,024=4 lets try another one 6^4/2 to solve it use the root formula 6^4/2=√6⁴=√1,296=36 lets try another one 7^0/4 to solve it use the root formula 7^0/4=⁴√7⁰=⁴√1=1 lets try last one 9^4/4=⁴√9⁴=⁴√6,561=9 now what if we used 6^3/0 wait on do not say its 1 anything dividied by 0 is not 0 here let me show you say we got a^n/0=⁰√aⁿ if n>0 (if a>1 (⁰√aⁿ=∞) else if a<-1 if n is even ((⁰√aⁿ=∞) else if n is odd (⁰√aⁿ=-∞)) else if |a|<1 (⁰√aⁿ=0)) else if n<0 if (a>1 (⁰√aⁿ=0) else if (a<-1 ⁰√aⁿ=0) else if (|a|<1 and a is pos (⁰√aⁿ=∞) else if a is neg if (n is even (⁰√aⁿ=∞) else if n is odd (⁰√aⁿ=-∞)))

Multiple Choice

26. 26. ⁰√9²

• -∞

• 81

• 1

• ∞

Multiple Choice

26. CHALLANGE 27. ^∞√666⁶⁶⁶

• 666

• ∞

• 1

• 0

Multiple Choice

26. 28. ^∞√2³

• 0

• 1

• 8

• 6

Multiple Choice

26. 29. ⁰√.9⁹

• .9

• ∞

• 1

• 0

Multiple Choice

26. 30. ⁶√262,144

• 1

• 2

• 3

• 8

​Exponents Grade 6+ Pt.7

​say i got an expression √(³√(729)) to do that we have to use the root product formula which is ⁿ√(^m√(a))=^nm√a why because this ⁿ√(^m√(a))=(^m√(a))^1/n=((a)^1/m)^1/n=a^1/mn=^nm√a see why now lets apply the same thing √(³√(729))=^2*3√729=⁶√729=3 another way to prove it is like this √(³√(729))=√9=3 i wont explain this way i want you to explain it on your own anyways lets try another one ³√(⁴√(1,000,000,000,000,000,000,000,000)) again multiply the roots like this ⁿ√(^m√(a))=^nm√a lets apply the same thing ³√(⁴√(1,000,000,000,000,000,000,000,000))=^3*4√1,000,000,000,000,000,000,000,000
=¹²√1,000,000,000,000,000,000,000,000=100 lets try the last one ⁶√³√262,144 same thing use the root formula ⁿ√(^m√(a))=^nm√a we can apply the same thing ⁶√³√262,144=^6*3√262,144=¹⁸√262,144=2 now i want you to try the rest of the excersies on your own and see how far you get

Multiple Choice

31. 31. ⁵√(³√(32,768))

• 16

• 4

• 2

• 8

Multiple Choice

32. CHALLANGE 32. √(√(√(√(65,536))))

• 2

• 16,384

• 4,096

• 8

Multiple Choice

33. 33. ³√(⁴√(4,096))

• 256

• 16

• 4

• 2

Multiple Choice

34. CHALLANGE 34. ⁷√(√(√(√(10¹¹²))))

• 10,000

• 1,000

• 100

• 10

Multiple Choice

35. 35. ⁵√(³√(√(10,000,000,000⁹)))

• 1

• 1,000

• 1,000,000

• 1,000,000,000

​Exponents Grade 6+ Pt.8

​say we got 81^.25 and we want to evaluate it so what we could do is to convert decimals into exponents so we know .25=1/4 so why wont you to do the same thing like you did in the past so we get 81^.25=81^1/4=⁴√81=3 plain simple lets try another one
729^.5 like we did previously convert decimals into fractions you can also convert percents into fractions using 2 steps anyhow .5=1/2 use the same interperatation we get 729^.5=729^1/2=√729=27 lets try another one 100,000,000^.25 same thing convert decimals to fractions we get .25=1/4 use the same interperatation we get 100,000,000^.25=100,000,000^1/4=⁴√100,000,000=100 lets try another one 2,401^.25 lets convert decimals in fractions we get .25=1/4 lets use the same interpretation on the ploblem we get we get 2,401^.25=2,401^1/4=⁴√2,401=7 lets try the last one 1,000,000,000^.7 again convert decimals into exponets we get .7=7/9 use the same interperation we get 1,000,000,000^.7=1,000,000,000^7/9=⁹√1,000,000,000⁷=⁹√1e+63
=10,000,000 now i want you to try the rest of the excerises on your own and see how far you get

Multiple Choice

36. 36. 1,000,000,000,000^0.25

• 1

• 1,000

• 1,000,000

• 1,000,000,000

Multiple Choice

37. 37. 6,561^0.5

• 1

• 9

• 81

• 729

Multiple Choice

38. 38. 64^0.16

• 2

• 4

• 1.94530989482

• 1.39474366635

Multiple Choice

39. 39. 6,561^0.625

• 27

• 81

• 243

• 729

Multiple Choice

40. 40. 100,000^0.2

• 1

• 10

• 100

• 1,000

​Exponents Grade 6+ Pt.9

​say i got an expression 4^50% and i want to evaluate it so what we do is to convert it into fraction we know 50%=0.5=1/2 so why wont we do the same thing so we get 4^50%=4^1/2=√4=2 lets try another one say i got 10,000,000,000^20% to evaluate it we have to convert percent into fraction heres the strategy 20%=0.2=1/5 lets do the same thing on you ploblem we get 10,000,000,000^20%=10,000,000,000^1/5
=⁵√10,000,000,000=100 lets try another one 6,561^12.5% to evaluate it we have to convert percent into fraction like always 12.5%=0.125=1/8 lets apply that in our ploblem we get 6,561^12.5%=6,561^1/8=⁸√6,561=3 lets try the last one 100,000,000^25% to evaluate it convert percent into fraction like always 25%=0.25= 1/4 lets apply that 100,000,000^25%=100,000,000^1/4=⁴√100,000,000=100 now i want you to try the rest of the excersies on your own and see how far you get good luck

Multiple Choice

41. 41. 729^66.6%

• 9

• 0.6

• 729

• 81

Multiple Choice

42. 42. 1,000^33.3%

• 1

• 0.3

• 10

• 333.3

Multiple Choice

43. 43. 256^75%

• 256

• 192

• 128

• 64

Multiple Choice

44. 44. 1,000,000^50%

• 100

• 1,000

• 1,000,000

• 1,000,000,000,000

Multiple Choice

45. 45. 64^83.3%

• 5,333.3

• 53.3

• 32

• 64

​Exponents Grade 6+ Pt.10

​say i got an equation (15n²)(5n⁴) and we want to mutliply both expression what we do so what were going to do is to seperate both the coefficients which is nonvariable or a number and variable a letter that stores a number we get (15n²)(5n⁴)=(15*5)(n²n⁴)=75n²⁺⁴=75n⁶ lets try another one (3x²y⁴)(3x³y³) to multiply samething seperate the coefficients and variable notice we got 2 variables so we must seperate them in order of how you like it but all variables must be all same if not the same than seperate them in parentases meaning you have to grupt them we get (3x²y⁴)(3x³y³)=(3*3)(x²x³)(y⁴y³)=9x⁵y⁷ lets try the last one (8x⁵y⁷z³)(4x²y³z⁷) what we do is the same thing we did in previous examples seperate coefficient nd variables group them we get(8x⁵y⁷z³)(4x²y³z⁷)=(8*4)(x⁵x²)(y⁷y³)(z³z⁷)=32x⁷y¹⁰z¹⁰ now i want you to try the rest of the excerises on your own and see how far you get

Multiple Choice

31. 46. (8u⁵v⁷)(15u¹⁰v¹²)

• 15u²⁰v¹⁹

• 8u²⁰v¹⁹

• 120u²⁰v¹⁹

• 120u¹⁵v¹⁹

Multiple Choice

32. 47. (7a²b⁴c⁶d⁸f¹⁰)(5ab²c⁴d⁸f¹⁶)

• 35a¹⁰b⁸c¹⁰d¹⁶f²⁶

• 35a³b⁶c¹⁰d¹⁶f²⁶

• 35a⁴b⁶c¹⁰d¹⁶f²⁶

• 35a²b⁸c¹⁰d¹⁶f²⁶

Multiple Choice

33. 48. 45(h⁶k⁷x²z⁴)(4h²k⁶x⁵z⁸)²

• 720h⁸k¹³x⁷z¹²

• 360h¹⁰k¹⁹x¹²z²⁰

• 360h⁸k¹³x⁷z¹²

• 720h¹⁰k¹⁹x¹²z²⁰

Multiple Choice

34. 49. 10(a²bc⁵)(a⁴b⁷c¹⁰)

• 10a⁶b⁸c¹⁵

• 10a⁸b⁷c⁵⁰

• 1,000a⁸b⁷c⁵⁰

• 1,000a⁶b⁸c¹⁵

Multiple Choice

45. CHALLANGE 50. (4x²y⁴z⁶)(5x¹⁵y⁴⁵z¹³⁵)

• 1,000x¹⁵y⁴⁷z¹³⁹

• 20x¹⁷y⁴⁹z¹⁴¹

• 1,000x¹⁵y⁴⁵z¹³⁵

• 20x²⁰y⁵⁰z¹³⁸

​Exponents Grade 6+ Pt.11

​lets say i got an equation 10z⁵/(5z³) and we want to simplify it so what we gonna do is to seperate like always so we get 10z⁵/(5z³)=(10/5)(z⁵/z³)=2z² now lets try another one 70x⁵y⁴/(7x²y³) first we must seperate them coefficient grouped same variable grouped up like this 70x⁵y⁴/(7x²y³)=(70/7)(x⁵/x²)(y⁴/y³)=10x³y lets try another one 80c³f³/(4c²f) first we must seperate them coefficient grouped same variable grouped up like this 80c³f³/(4c²f)=(80/4)(c³/c²)(f³/f)=20cf² lets try another one 4o³k²/(10o⁵k³) first we must seperate them coefficient grouped same variable grouped up like this 4o³k²/(10o⁵k³)=(4/10)(o³/o⁵)(k²/k³)=(2/5)(1/o²)(1/k)=2/(5o²k) lets try the last one 7u²v⁴w²/(35u³v²w) first we must seperate them coefficient grouped same variable grouped up like this 7u²v⁴w²/(35u³v²w)
=(7/35)(u²/u³)(v⁴/v²)(w²/w)=(1/5)(1/u)(v²)(w)=v²w/(5u) now i want you to try the rest of the excersises on your own and see how far you get

Multiple Choice

51. 51. 45x²y⁵/(9xy⁷)

• 5y¹²/x³

• 5x³y¹²

• 5xy²

• 5x/y²

Multiple Choice

52. 52. 7u²v⁴w⁷/(7u⁴w⁶)

• 7v⁴w/u²

• v⁴w/u²

• u²v⁴w

• 7u²v⁴w

Multiple Choice

53. 53. 60h²k²l⁵/(5hkl)

• 12h³k³l⁶

• 12hkl⁴

• 300hkl⁴

• 300h³k³l⁶

Multiple Choice

54. 54. 80t²u⁵/(16t²u²)

• 5u³

• 5t⁴u⁷

• 5t²*√u⁷

• 5t²u⁵

Multiple Choice

55. 55. 100p²q/(10p⁵q¹⁰)

• /(10p³q⁹)

• p⁷q¹¹/(10)

• 10/p³q⁹

• 10p⁷q¹¹

​Exponents Grade 6+ Pt.12

​lets say i got an equation (5x²y³)³ and we want to solve it to do that we need to separate them or use the rule (aⁿb^m)^k=a^nkb^mk (aⁿb^m)^k=(aⁿ)^k(b^m)^k=a^nkb^mk or we get (5x²y³)³=(5)³(x²)³(y³)³=125x^2*3y^3*3=125x⁶y⁹ lets try another one say i got (9u⁴v⁵)⁴ to solve it we separate them we get (9u⁴v⁵)⁴=(9)⁴(u⁴)⁴(v⁵)⁴==6,561u^4*4v^5*4=6,561u¹⁶v²⁰ lets try another one (8x⁵y⁴)² to solve it we seperate them we get (8x⁵y⁴)²=(8)²(x⁵)²(y⁴)²=64x^5*2y^4*2=64x¹⁰y⁸ lets try the last one (3p³s⁴h⁸d²a⁶)⁶ to solve it we seperate them we get (3p³s⁴h⁸d²a⁶)⁶=(3)⁶(p³)⁶(s⁴)⁶(h⁸)⁶(d²)⁶(a⁶)⁶=729p^3*6s^4*6h^8*6d^2*6a^6*6=729p¹⁸s²⁴h⁴⁸d¹²a³⁶
now i want you to try the rest of the excerises on your own and see how far you get

Multiple Choice

56. 56. (a/b)³

• a³/b³

• ab³

• a³b³

• a³b

Multiple Choice

57. 57. (3r^60%s^40%)⁵(5r⁴s¹⁰)²

• 40,000,000r²²s⁴⁴

• 40,025,750r²²s⁴⁴

• 6,600r¹¹s²²

• 6,075r¹¹s²²

Multiple Choice

58. CHALLANGE 58. ((w²v⁴y²z⁵)²)³(2w⁵v³y/z)²

• 62,500w¹¹v¹⁵y⁷z¹⁴

• 60,000w²²v³⁰y¹⁴z²⁸

• 62,500w²²v³⁰y¹⁴z²⁸

• 60,000w¹¹v¹⁵y⁷z¹⁴

Multiple Choice

59. 59. (a²b²c²)⁶

• a³b³c³

• a⁶b⁶c⁶

• a¹²b¹²c¹²

• a²⁴b²⁴c²⁴

Multiple Choice

60. CHALLANGE 60. 5(3a³b²c)²(2a³b⁴c⁵)(4ab²c³)³(a^15%b^10%c^5%)²⁰

• 5,760a¹⁵b¹⁶c¹⁷

• 5,760a²⁰b¹⁶c¹⁷

• 120a¹⁰b¹⁰c¹⁰

• 5,760a¹⁰b¹⁰c¹⁰

​Exponents Grade 6+ Pt.13

​lets say i got ⁵√(q⁵u⁵t¹⁰s¹⁵) and i want to simplify it so what we do is to convert it into fractional exponent remember the rule a^n/m=^m√aⁿ let try getting an exponent on our ploblem we get ⁵√(q⁵u⁵t¹⁰s¹⁵)=⁵√(q⁵u⁵t¹⁰s¹⁵)¹ convert into fractional exponent we get ⁵√(q⁵u⁵t¹⁰s¹⁵)=⁵√(q⁵u⁵t¹⁰s¹⁵)¹=(q⁵u⁵t¹⁰s¹⁵)^1/5=(q⁵)^1/5(u⁵)^1/5(t¹⁰)^1/5(s¹⁵)^1/5
=q^5*1/5u^5*1/5t¹⁰*^1/5s¹⁵*^1/5=qut²s³ lets try another one ³√(a³b³c⁹)² first to convert root in to exponintial fraction we get ³√(a³b³c⁹)²=((a³b³c⁹)²)^1/3=(a³b³c⁹)^2*1/3=(a³b³c⁹)^2/3
=(a³b³c⁹)^2/3=(a³)^2/3(b³)^2/3(c⁹)^2/3=a³*^2/3b^3*2/3c^9*2/3=a^6/3b^6/3c^18/3=a²b²c⁶ lets try the last one ⁵√(243h⁵j³l⁴m²)³ first to convert root in to exponintial fraction we get ⁵√(243h⁵j³l⁴m²)³=((243h⁵j³l⁴m²)³)^1/5=(243h⁵j³l⁴m²)^3*1/5=(243h⁵j³l⁴m²)^3/5=(243)^3/5(h⁵)^3/5(j³)^3/5(l⁴)^3/5(m²)^3/5=243^3/5h^5*3/5j^3*3/5l^4*3/5m^2*3/5
=3³h^15/5j^9/5l^12/5m^6/5=27h³j^9/5l^12/5m^6/5 now i want you to try the rest of the excersizes on your own and see how far you get

Multiple Choice

61. 61. √(9h²k⁶m⁴o¹⁰)³

• 27h²k⁶m⁴o¹⁰

• 9h²k⁶m⁴o¹⁰

• 9h³k⁹m⁶o¹⁵

• 27h³k⁹m⁶o¹⁵

Multiple Choice

62. CHALLANGE 62. ³√((⁵√n³)(⁷√p⁸))⁷

• (⁵√n⁷)(³√p⁸)

• (³√n⁸)(³√p⁸)

• (⁵√n⁷)(⁵√p⁷)

• (³√n⁸)(⁵√p⁷)

Multiple Choice

63. 63. (⁷√(128o⁵⁶w⁶³y³⁵)⁵)(√(o⁵⁶w⁶⁰y¹⁰)⁴)

• 63. 128o¹⁵²w¹⁶⁵y⁴⁵

• 63. 32(⁵√o¹⁰⁶⁴)w²³¹y⁶³

• 63. 128(⁵√o¹⁰⁶⁴)w²³¹y⁶³

• 63. 32o¹⁵²w¹⁶⁵y⁴⁵

Multiple Choice

64. 64. (³√(√r⁹(√(√(t⁶))))²)(√((³√r⁵)(³√t²)²)⁶)

• 64. r⁸t⁵

• 64. r²t⁵

• 64. r⁸t²

• 64. r⁵t²

Multiple Choice

65. CHALLANGE 65. (⁷√(h⁴r⁴t⁶u⁷x⁴y⁸z⁹)³)(³√(8h⁸r⁴t²u⁶x⁷y²z⁴)⁴)

• 16u¹¹(²¹√(h²⁶⁰r¹⁴⁸t¹¹⁰x²³²y¹²⁸z¹⁹³))

• 16u¹¹(²¹√(h²⁶⁰r¹⁴⁸t¹¹⁰x²³⁷y¹³¹z²⁰⁰))

• 16u⁸(²¹√(h²⁶⁰r¹⁵⁷t¹¹⁵x²⁴²y¹³⁴z²⁰⁶))

• 16u⁸(²¹√(h²⁶⁰r¹⁴⁸t¹¹⁹x²⁴⁷y¹³⁹z²¹³))

​Exponents Grade 6+ Pt.14

​lets try (v¹²x⁹)^0.3 to solve that we must convert decimals into fraction we get 0.3=1/3
lets apply that we get (v¹²x⁹)^0.3=(v¹²x⁹)^1/3=(v¹²x⁹)^1/3=(v¹²)^1/3(x⁹)^1/3=v^12*1/3x^9*1/3=v⁴x³ lets try another one (n⁵h⁵)^.4 to solve that like what we did previously we must convert decimals into fraction we get .4=2/5 lets apply that just like previously we get (n⁵h⁵)^.4=(n⁵h⁵)^2/5=(n⁵h⁵)^2/5=(n⁵)^2/5(h⁵)^2/5=n^5*2/5h^5*2/5=n²h² lets try another one (512x⁹64y⁶)^0.6 to solve that like what we did previously we must convert decimals into fraction we get 0.6=2/3 lets apply that just like previously we get (32,768x⁹y⁶)^0.6
=(32,768x⁹y⁶)^2/3=(32,768x⁹y⁶)^2/3=(32,768)^2/3(x⁹)^2/3(y⁶)^2/3
=1,024x^9*2/364^2/3y^6*2/3=64x⁶16y⁴=1,024x⁶y⁴ lets try the last one (256a³²b⁴⁰)^0.875 to solve that like what we did previously we must convert decimals into fraction we get
0.875=7/8 lets apply that just like previously we get (256a³²b⁴⁰)^0.875=(256a³²b⁴⁰)^7/8=(256)^7/8(a³²)^7/8(b⁴⁰)^7/8=128a^32*7/8b^40*7/8=128a²⁸b³⁵ now i want you to try the rest of these excerisies on your own and see how far you get good luck

Multiple Choice

66. 66. (32s⁵t⁵u⁵)^0.8

• 66. 25.6s⁵t⁵u⁵

• 66. 32s⁵t⁵u⁵

• 66. 12.8s⁴t⁴u⁴

• 66. 16s⁴t⁴u⁴

Multiple Choice

67. CHALLANGE 67. ³√((√(x³y⁶z⁹)^0.5)⁶(⁵√(xy²z³))¹⁰)⁴

• (z(³√(xy²)))²⁶

• (⁶√(xy²z³))¹³

• (⁶√(xy²z³))

• (z(³√(xy²)))

Multiple Choice

68. 68. ⁴√(1,024n²⁰s³⁰)^0.9

• 68. 8(√(n⁹(√(2s²⁷))))

• 68. 2(√(n⁹(√(2s²⁷))))

• 68. 4(√(n⁹(√(2s²⁷))))

• 68. (√(n⁹(√(2s²⁷))))

Multiple Choice

69. CHALLANGE 69. ^0.25√(√(h^0.5b²))

• hb⁴

• h^0.0625b^0.25

• (hb)^0.25

• hb

Multiple Choice

70. 70. √(√(m³²h⁴⁸))^0.25

• m²h³

• 70. m³²h⁴⁸

• m⁵¹²h⁷⁶⁸

• m⁸h¹²

​Exponents Grade 6+ Pt.15

​lets try (w⁸y⁷)^20% to solve it we must convert percents into fractions we get
20%=1/5 so (w⁸y⁷)^20%=(w⁸y⁷)^1/5=(w⁸)^1/5(y⁷)^1/5=w^8*1/5y^7*1/5=w^8/5y^7/5=(⁵√w⁸)(⁵√y⁷)=⁵√(w⁸y⁷) lets try another one (f⁵x³)^33.3% to solve it we must convert percents into fractions we get 33.3%=1/3 so(f⁵x³)^33.3%=(f⁵x³)^1/3=(f⁵)^1/3(x³)^1/3=f^5*1/3x^3*1/3
=f^5/3x=x(³√f⁵) lets try another one (m²⁵s⁵⁰)^28% to solve it we must convert percents into fractions we get 28%=7/25 so (m²⁵s⁵⁰)^28%=(m²⁵s⁵⁰)^7/25=(m²⁵)^7/25(s⁵⁰)^7/25=m^25*7/25s^50*7/25=m⁷s¹⁴ lets try another one (d⁵⁵s⁵⁵)^40% to solve it we must convert percents into fractions we get 40%=2/5 so (d⁵⁵s⁵⁵)^40%=(d⁵⁵s⁵⁵)^2/5=d^55*2/5s^55*2/5=d²²s²² lets try the last one (opq³)^16.6% to solve it we must convert percents into fractions we get 16.6%=1/6 so (opq³)^16.6%=(opq³)^1/6=(o)^1/6(p)^1/6(q³)^1/6=o^1/6p^1/6q^3*1/6=o^1/6p^1/6q^1/2=(⁶√o)(⁶√p)(√q)=(⁶√o)(⁶√p)(√q)=√(q(³√(op))) now i want you to try the rest of the excerises on your own and see how far you get

Multiple Choice

71. 71. ^50%√(a²b²c²)^25%

• abc

• a²b²c²

• a⁴b⁴c⁴

• a⁸b⁸c⁸

Multiple Choice

71. 72. ^50%√(^50%√(ds))^25%

• ds

• d²s²

• d⁴s⁴

• d⁸s⁸

Multiple Choice

71. 73. ^6.25%√(xyz)^25%

• 71. xyz

• 71. x²y²z²

• 71. x⁴y⁴z⁴

• 71. x⁸y⁸z⁸

Multiple Choice

71. CHALLANGE 74. ⁵√((^10%√(xyz)^250%)(^20%√(y√z⁵)^1000%))^20%

• 71. xy³z⁶

• 71. z¹⁵√(x⁵y¹⁵)

• 71. x⁵y¹⁵z³⁰

• 71. x²⁵y⁷⁵z¹⁵⁰

Multiple Choice

71. 75. ^20%√(o^20%w^10%)^100%

• o√w

• ow

• o⁵(√w⁵)

• o⁵w⁵

Multiple Choice

71. 76. 2^2x+3=2^7x+8 find the value of x

• -2

• -1

• 1

• 2

Multiple Choice

71. 77. 125^c+1=5^2c+1 find the value of c

• -2

• -1

• 1

• 2

Multiple Choice

71. CHALLANGE 78. ^g√4=16 find the value of g 4=2/x.

• 1/4

• 1/2

• 2

• 4

Multiple Choice

71. CHALLANGE 79. ^√u√2=65,536 find the value of u

• 1/4

• 1/2

• 2

• 4

Multiple Choice

71. 80. 5/5^|t|=4% find the value of t

• t=0

• t=1, t=-1

• t=2, t=-2

• t=3, t=-3