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

- anonymous

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- anonymous

@phi

- anonymous

@IrishBoy123 @imqwerty

- anonymous

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

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## More answers

- phi

what does a negative exponent mean ? any idea ?

- anonymous

Just like a regular exponent just negative?

- phi

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

- anonymous

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

- phi

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

- anonymous

This is a combo of both lol

- anonymous

hmm

- phi

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

- anonymous

its a negative exponent?

- phi

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

- anonymous

..

- anonymous

the 1 is the exponent?

- anonymous

right

- phi

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

- anonymous

umm

- anonymous

maybe

- 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)

- anonymous

so like 1-2?

- anonymous

like the - sign is negative?

- anonymous

i do not get it D:

- 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

- phi

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

- anonymous

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

- anonymous

or the 1/2

- anonymous

ok i think i got that

- phi

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

- anonymous

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

- phi

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

- anonymous

lets see

- anonymous

2/3?

- anonymous

or 2^-3?

- anonymous

ya 2/3 that would be correct i believe

- 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

- anonymous

mm

- anonymous

its still really confusing

- phi

let's try this
flip 1/2

- anonymous

1^2?

- anonymous

1^-2

- anonymous

im sorry D:

- phi

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

- anonymous

the 1

- phi

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

- anonymous

2/1

- phi

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

- anonymous

1/2?

- phi

yes
can you flip 1/3 ?

- anonymous

ohhhh ok 31

- anonymous

3/1*

- phi

yes

- anonymous

ahhhhh ok

- 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

- anonymous

mm

- phi

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

- anonymous

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

- phi

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

- anonymous

ok

- anonymous

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

- phi

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

- anonymous

hmm so the 1/2-5

- anonymous

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

- phi

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

- anonymous

ok

- anonymous

still really weird to me

- 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

- anonymous

ok

- phi

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

- phi

*treat

- anonymous

ok umm 3/7

- 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 ?

- anonymous

ok lets see

- anonymous

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

- phi

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

- anonymous

ok

- anonymous

so 3/7^-2?

- anonymous

or 3^7-2

- phi

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

- anonymous

ohhh

- anonymous

7^3 stays the same

- anonymous

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

- phi

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

- anonymous

ohhhh

- anonymous

ok so the 7 stays with the 3

- anonymous

ok ok

- phi

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

- anonymous

ya

- phi

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

- anonymous

no i didnt

- phi

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

- anonymous

yes

- phi

and 5^2 means 5*5

- anonymous

yes

- phi

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

- anonymous

hmm

- anonymous

I was think 7x3x2 but that wouldnt be correct right

- 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 ?

- anonymous

7x3 and 3x2?

- phi

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

- anonymous

thats how it is??

- anonymous

there is only 1 7^3

- 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

- anonymous

hmmm ok

- phi

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

- anonymous

ok

- anonymous

so it would be 7x7x7?

- anonymous

if I understand correctly or 7x3?

- phi

7^3 means 7*7*7

- anonymous

ok i got that

- 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
\[ \left(7^3\right)^{-2}= \frac{1}{7\cdot 7\cdot 7\cdot 7\cdot 7\cdot 7} \]

- anonymous

ohhhh

- anonymous

:DDD

- anonymous

THANK YOUU

- anonymous

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

- phi

if you make a new post

- anonymous

i will!

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