## anonymous one year ago I really need help I don't have a math teacher so I'm trying learn this on my on so please someone help What is 16 5/4 in simplest form? There more questions but I'm putting the file down in the comments.

1. anonymous

2. phi

simplest form is a bit vague. But as a rule, if you see a fraction like $\frac{5}{4}$ where the top is bigger than the bottom, that is an "improper fraction" which means people would rather see it written as a mixed number can you write 5/4 as a mixed number?

3. anonymous

4. anonymous

i guess

5. phi

5/4 means divide 4 into 5, plus a remainder that you "put over" 4

6. anonymous

if you divide 4 into 5 it's 0.8

7. phi

that is 4/5 = 0.8 in other words you did 5 divided into 4

8. anonymous

either I'm stupid or i just don't get what you're saying

9. phi

Can you post a copy of the question?

10. anonymous

yes hold on

11. anonymous

12. anonymous

What he's trying to say is you need to do the problem 5 divided by 4 as a starter

13. phi

oh, that is different from what I thought 5/4 is an exponent

14. anonymous

Oh same here :/

15. anonymous

5 divided by 4 is 1.25

16. anonymous

Ok so basically this problem is asking what is 16 to the power of 1.25 right @phi

17. phi

yes, 5/4 = 1.25 but that is not the problem we have to solve here the way we solve this is write the problem as $\left( 16^\frac{1}{4}\right)^5$ the 1/4 power means the "fourth root"

18. anonymous

Right

19. phi

to find the 4th root (which is generally hard to do, but possible here) we should factor 16 into 2*2*2*2 = $$2^4$$

20. phi

do you see that 2 times itself 4 times is 16 ?

21. anonymous

81?

22. phi

so we write 16 as 2^4 $\left( 16^\frac{1}{4}\right)^5 = \left( (2^4)^\frac{1}{4}\right)^5$

23. phi

now use the rules of exponents we use this rule $(a^b)^c = a^{bc}$ on $(2^4)^\frac{1}{4}$ can you do that ?

24. anonymous

I'm stupid and lost

25. anonymous

do 2x2x2x2

26. anonymous

right?

27. phi

the rule $$(a^b)^c = a^{bc}$$ means if you have an exponent b and another exponent c , we can multiply them

28. phi

you "match the pattern" $(a^b)^c = a^{bc} \\ (2^4)^\frac{1}{4}$

29. phi

we could do 2*2*2*2 but we don't want to (because if we use the exponent rule we will get a simpler answer)

30. phi

look at these two things $(a^b)^c = a^{bc} \\ (2^4)^\frac{1}{4}$ do you see you can match a with 2, and 4 with b, and 1/4 with c ?

31. phi

the idea is we can rewrite (2^4)^(1/4) using that rule $2^{4 \cdot \frac{1}{4} }$

32. anonymous

i see numbers that's makes no sense to why the hell letters are in a math problem and we are talking about 16 and a 5/4 so where in the world did a 2 and a 1 come form

33. anonymous

I'm sorry that im getting mad and rude but i've been doing this all day and been have to learn this on my on

34. phi

the letters are how to show a "rule" we could use words, but it gets confusing. anyway, we started with $16^\frac{5}{4}$ we use a "rule" to write that a different way $(16^\frac{1}{4})^5$ before going on, do you know what 1/4 * 5 is ?

35. anonymous

1/4

36. phi

$\frac{1}{4} \cdot 5 = ?$ (as an improper fraction)

37. anonymous

sorry 1.25

38. phi

ok, but not as a decimal. what about as a fraction ?

39. anonymous

no i dont i just know what it is as a decimal because my phone told me

40. phi

when you multiply fractions, you multiply top times top and bottom times bottom (if a number (like the 5) has no "bottom" , assume it is 1) now try again $\frac{1}{4} \cdot 5=?$

41. anonymous

5/4

42. phi

yes. the reason we want to know that is we can say $\frac{5}{4}= \frac{1}{4} \cdot 5$ and vice versa

43. phi

and there is a rule that let's us write $16^\frac{5}{4} = (16^\frac{1}{4})^5$

44. anonymous

so now i know where you got 1/4

45. phi

if you see $(16^\frac{1}{4})^5$ you should remember you are allowed to write it as $16^\frac{5}{4}$ we need to be able to between these two different ways

46. phi

so far we have $(16^\frac{1}{4})^5$ the next thing is to know we can write 16 as 2*2*2*2 (this is the hard part, knowing that. but now you do. (don't forget) )

47. phi

do you know how to use the "short-cut" way using exponents to write 2*2*2*2 ? in other words that is 2^?

48. phi

2*2*2*2 is 2 to some power (some exponent) do you know what little number we should put in the upper right of 2 so that it means 2*2*2*2 ?

49. anonymous

50. phi

do you know $$2^1 = 2$$ and $$2^2 = 2\cdot 2$$ and $$2^3 = 2\cdot 2\cdot 2$$ ?

51. anonymous

yes

52. phi

ok, so how do we write $2\cdot 2\cdot 2\cdot 2= 2^?$

53. anonymous

2 to the 4 power

54. phi

ok, so we know 16= 2*2*2*2 and that is 2^4

55. phi

$(16^\frac{1}{4})^5 \\ ((2^4)^\frac{1}{4})^5$

56. phi

now let's use the rule on $(2^4)^\frac{1}{4}$ remember we can multiply the exponents ?

57. anonymous

so I multiply 2^4 by 1/4?

58. phi

you multiply the exponents , so just 4*1/4 and that is the new exponent

59. anonymous

1

60. phi

that means $(2^4)^\frac{1}{4} = 2^1$

61. phi

so now we have this $(16^\frac{1}{4})^5 \\ ((2^4)^\frac{1}{4})^5 \\ (2^1)^5$ notice we can use the rule again to multiply the exponents on the last line

62. anonymous

(2^1)5 is 10

63. phi

no, not 10 it is (2^1)^5 i.e. $$(2^1)^5$$ multiply the exponents (that means 1 and 5)

64. anonymous

5

65. phi

yes, and that means 5 is the new exponent. so (2^1)^5 = 2^5 ok ?

66. anonymous

okay i get that

67. phi

they may want you to multiply that out for the final answer what is 2 times itself 5 times ?

68. anonymous

32

69. phi

70. anonymous

thank you so much for helping me and last question are you a math teacher?

71. phi

no

72. anonymous

you need to be