Question

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

Answer 1

@phi

Answer 2

@IrishBoy123 @imqwerty

Answer 3

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

Answer 4

what does a negative exponent mean ? any idea ?

Answer 5

Just like a regular exponent just negative?

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

This is a combo of both lol

Answer 10

hmm

Answer 11

you can learn it if you have time

try guessing what \( 2^{-1} \) is. (flip it and negative the exponent)

Answer 12

its a negative exponent?

Answer 13

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

Answer 14

..

Answer 15

the 1 is the exponent?

Answer 16

right

Answer 17

can you rewrite \( 2^{-1} \)
?

Answer 18

umm

Answer 19

maybe

Answer 20

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

if you have (stuff) write 1/(stuff)

Answer 21

so like 1-2?

Answer 22

like the - sign is negative?

Answer 23

i do not get it D:

Answer 24

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

Answer 25

\[ 2^{-1} = \frac{1}{2^1} = \frac{1}{2} \]

Answer 26

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

Answer 27

or the 1/2

Answer 28

ok i think i got that

Answer 29

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

Answer 30

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

Answer 31

ok, one more

\[ 3^{-2} \]
can you flip and negate the exponent?

Answer 32

lets see

Answer 33

2/3?

Answer 34

or 2^-3?

Answer 35

ya 2/3 that would be correct i believe

Answer 36

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

Answer 37

mm

Answer 38

its still really confusing

Answer 39

let's try this
flip 1/2

Answer 40

1^2?

Answer 41

1^-2

Answer 42

im sorry D:

Answer 43

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

Answer 44

the 1

Answer 45

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

Answer 46

2/1

Answer 47

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

Answer 48

1/2?

Answer 49

yes

can you flip 1/3 ?

Answer 50

ohhhh ok 31

Answer 51

3/1*

Answer 52

yes

Answer 53

ahhhhh ok

Answer 54

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

Answer 55

mm

Answer 56

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

Answer 57

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

Answer 58

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

Answer 59

ok

Answer 60

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

Answer 61

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

Answer 62

hmm so the 1/2-5

Answer 63

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

Answer 64

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

Answer 65

ok

Answer 66

still really weird to me

Answer 67

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

Answer 68

ok

Answer 69

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

Answer 70

*treat

Answer 71

ok umm 3/7

Answer 72

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 ?

Answer 73

ok lets see

Answer 74

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

Answer 75

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

Answer 76

ok

Answer 77

so 3/7^-2?

Answer 78

or 3^7-2

Answer 79

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

Answer 80

ohhh

Answer 81

7^3 stays the same

Answer 82

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

Answer 83

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

Answer 84

ohhhh

Answer 85

ok so the 7 stays with the 3

Answer 86

ok ok

Answer 87

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

Answer 88

ya

Answer 89

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

Answer 90

no i didnt

Answer 91

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

Answer 92

yes

Answer 93

and 5^2 means 5*5

Answer 94

yes

Answer 95

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

Answer 96

hmm

Answer 97

I was think 7x3x2 but that wouldnt be correct right