## anonymous one year ago Which expression is equivalent to (7^3)−2? 1 over 7 times 7 times 7 times 7 times 7 times 7 7 1 over 7 negative 1 over 7 times 7 times 7 times 7 times 7 times 7

1. anonymous

@phi

2. anonymous

@IrishBoy123 @imqwerty

3. anonymous

I need help with some exponent questions if you can help that'd be awesome

4. phi

what does a negative exponent mean ? any idea ?

5. anonymous

Just like a regular exponent just negative?

6. phi

there is a long explanation of why it is so, but cutting to the chase $a^{-b}= \frac{1}{a^b}$ and $a^{b}= \frac{1}{a^{-b}}$

7. anonymous

hmm i get confused with fractions and exponents so I really dont know

8. phi

that "rule" says: flip the fraction *and* negate the exponent.

9. anonymous

This is a combo of both lol

10. anonymous

hmm

11. phi

you can learn it if you have time try guessing what $$2^{-1}$$ is. (flip it and negative the exponent)

12. anonymous

its a negative exponent?

13. phi

$$2^{-1}$$ has an exponent of -1 you can "rewrite it" by 1) flipping it 2) make the exponent -(-1) = +1

14. anonymous

..

15. anonymous

the 1 is the exponent?

16. anonymous

right

17. phi

can you rewrite $$2^{-1}$$ ?

18. anonymous

umm

19. anonymous

maybe

20. phi

flip (invert) means if you have a, write 1/a if you have 1/a write a if you have (stuff) write 1/(stuff)

21. anonymous

so like 1-2?

22. anonymous

like the - sign is negative?

23. anonymous

i do not get it D:

24. phi

2^(-1) first step: FLIP 1/2^(-1)) second step: change the exponent -1 to -(-1) (which simplifies to 1) we get 1/2^1 or just 1/2

25. phi

$2^{-1} = \frac{1}{2^1} = \frac{1}{2}$

26. anonymous

ok so the 2^-1 would be 1^-2?

27. anonymous

or the 1/2

28. anonymous

ok i think i got that

29. phi

if you just had 3 $3 \text{ flipped is } \frac{1}{3}$

30. anonymous

so instead of 1^-3 itd be 1/3??

31. phi

ok, one more $3^{-2}$ can you flip and negate the exponent?

32. anonymous

lets see

33. anonymous

2/3?

34. anonymous

or 2^-3?

35. anonymous

ya 2/3 that would be correct i believe

36. phi

none of those. you don't change 3^-2 when you flip it rather, we think of it as $\frac{3^{-2}}{1}$ and swap top and bottom to flip it. then change the -2 to +2

37. anonymous

mm

38. anonymous

its still really confusing

39. phi

let's try this flip 1/2

40. anonymous

1^2?

41. anonymous

1^-2

42. anonymous

im sorry D:

43. phi

in $$\frac{1}{2}$$ what is the top number ?

44. anonymous

the 1

45. phi

and 2 is the bottom number. what do you get if you swap those ?

46. anonymous

2/1

47. phi

and what do you get if you flip 2/1 ?

48. anonymous

1/2?

49. phi

yes can you flip 1/3 ?

50. anonymous

ohhhh ok 31

51. anonymous

3/1*

52. phi

yes

53. anonymous

ahhhhh ok

54. phi

normally when we flip a number, say 2 to 1/2 we get different numbers. (2 is not 1/2) but if we *also* change its exponent, we get the same number

55. anonymous

mm

56. phi

in other words $2^{-1}$ if we flip it , to get $$\frac{1}{2^{-1}}$$ and then change the -1 to +1, $2^{-1}=\frac{1}{2}$

57. anonymous

ok so we pretty much eliminate the -1? if we do +1?

58. phi

another example $2^{-5} = \frac{1}{2^5}$

59. anonymous

ok

60. anonymous

then if we changed the exponent to +5 it'd go as 1/2?

61. phi

I don't understand the question. can you ask in a different way?

62. anonymous

hmm so the 1/2-5

63. anonymous

if we changed the -5 to +5 then instead of 1/2-5 it would be 1/2?

64. phi

$\frac{1}{2^{-5}}$ 1) flip it and 2) change the sign on the 5 we get $\frac{1}{2^{-5}} =2^5$

65. anonymous

ok

66. anonymous

still really weird to me

67. phi

it all makes sense (once you learn what is going on) but for the moment, just learn the rules 2^5 can be written as 1/2^-5 2^-5 can be written as 1/2^5

68. anonymous

ok

69. phi

$(7^3)^{−2}$ can you rewrite this? (tread the (7^3) as one thing)

70. phi

*treat

71. anonymous

ok umm 3/7

72. phi

leave (7^3) alone. it is one thing. keep it one thing. but if we do (7^3)^ -2 what can we do to make the -2 positive ?

73. anonymous

ok lets see

74. anonymous

i believe flip the numbers around? I really dont know DD:

75. phi

yes flip. think of (7^3) as one "number"

76. anonymous

ok

77. anonymous

so 3/7^-2?

78. anonymous

or 3^7-2

79. phi

you changed (7^3) . don't change it.

80. anonymous

ohhh

81. anonymous

7^3 stays the same

82. anonymous

if we made it different it would be 7/3^2?

83. phi

yes, what changes is we write 1/(7^3)^2

84. anonymous

ohhhh

85. anonymous

ok so the 7 stays with the 3

86. anonymous

ok ok

87. phi

we now have $\frac{1}{(7^3)^2}$

88. anonymous

ya

89. phi

do you know that x^2 means x*x ?

90. anonymous

no i didnt

91. phi

do you know that 3^2 means 3*3 ?

92. anonymous

yes

93. phi

and 5^2 means 5*5

94. anonymous

yes

95. phi

what about (7^3)^2 any idea ?

96. anonymous

hmm

97. anonymous

I was think 7x3x2 but that wouldnt be correct right

98. phi

use the same pattern as 2^2 = 2*2 3^2 = 3*3 4^2 = 4*4 x^2 = x*x y^2 = y*y do you see how to do (7^3)^2 ?

99. anonymous

7x3 and 3x2?

100. phi

would you believe (7^3)*(7^3) ?

101. anonymous

thats how it is??

102. anonymous

there is only 1 7^3

103. phi

if you have something and want to say: multiply by itself 2 times, you write (something)^2 and that is short for something * something

104. anonymous

hmmm ok

105. phi

so you want to show (xyz) times itself 3 times you would write (xyz)^3

106. anonymous

ok

107. anonymous

so it would be 7x7x7?

108. anonymous

if I understand correctly or 7x3?

109. phi

7^3 means 7*7*7

110. anonymous

ok i got that

111. phi

so (7^3)^2 means (7^3)*(7^3) and 7^3 means 7*7*7 so we can say (7*7*7)*(7*7*7) or just 7*7*7*7*7*7 so $\left(7^3\right)^{-2}= \frac{1}{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7}$

112. anonymous

ohhhh

113. anonymous

:DDD

114. anonymous

THANK YOUU

115. anonymous

btw I have a few more if you can help:?

116. phi

if you make a new post

117. anonymous

i will!