anonymous
  • anonymous
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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@phi
anonymous
  • anonymous
@IrishBoy123 @imqwerty
anonymous
  • anonymous
I need help with some exponent questions if you can help that'd be awesome

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phi
  • phi
what does a negative exponent mean ? any idea ?
anonymous
  • anonymous
Just like a regular exponent just negative?
phi
  • 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
  • anonymous
hmm i get confused with fractions and exponents so I really dont know
phi
  • phi
that "rule" says: flip the fraction *and* negate the exponent.
anonymous
  • anonymous
This is a combo of both lol
anonymous
  • anonymous
hmm
phi
  • phi
you can learn it if you have time try guessing what \( 2^{-1} \) is. (flip it and negative the exponent)
anonymous
  • anonymous
its a negative exponent?
phi
  • phi
\( 2^{-1} \) has an exponent of -1 you can "rewrite it" by 1) flipping it 2) make the exponent -(-1) = +1
anonymous
  • anonymous
..
anonymous
  • anonymous
the 1 is the exponent?
anonymous
  • anonymous
right
phi
  • phi
can you rewrite \( 2^{-1} \) ?
anonymous
  • anonymous
umm
anonymous
  • anonymous
maybe
phi
  • 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
  • anonymous
so like 1-2?
anonymous
  • anonymous
like the - sign is negative?
anonymous
  • anonymous
i do not get it D:
phi
  • 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
  • phi
\[ 2^{-1} = \frac{1}{2^1} = \frac{1}{2} \]
anonymous
  • anonymous
ok so the 2^-1 would be 1^-2?
anonymous
  • anonymous
or the 1/2
anonymous
  • anonymous
ok i think i got that
phi
  • phi
if you just had 3 \[ 3 \text{ flipped is } \frac{1}{3} \]
anonymous
  • anonymous
so instead of 1^-3 itd be 1/3??
phi
  • phi
ok, one more \[ 3^{-2} \] can you flip and negate the exponent?
anonymous
  • anonymous
lets see
anonymous
  • anonymous
2/3?
anonymous
  • anonymous
or 2^-3?
anonymous
  • anonymous
ya 2/3 that would be correct i believe
phi
  • 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
  • anonymous
mm
anonymous
  • anonymous
its still really confusing
phi
  • phi
let's try this flip 1/2
anonymous
  • anonymous
1^2?
anonymous
  • anonymous
1^-2
anonymous
  • anonymous
im sorry D:
phi
  • phi
in \( \frac{1}{2} \) what is the top number ?
anonymous
  • anonymous
the 1
phi
  • phi
and 2 is the bottom number. what do you get if you swap those ?
anonymous
  • anonymous
2/1
phi
  • phi
and what do you get if you flip 2/1 ?
anonymous
  • anonymous
1/2?
phi
  • phi
yes can you flip 1/3 ?
anonymous
  • anonymous
ohhhh ok 31
anonymous
  • anonymous
3/1*
phi
  • phi
yes
anonymous
  • anonymous
ahhhhh ok
phi
  • 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
  • anonymous
mm
phi
  • 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
  • anonymous
ok so we pretty much eliminate the -1? if we do +1?
phi
  • phi
another example \[ 2^{-5} = \frac{1}{2^5} \]
anonymous
  • anonymous
ok
anonymous
  • anonymous
then if we changed the exponent to +5 it'd go as 1/2?
phi
  • phi
I don't understand the question. can you ask in a different way?
anonymous
  • anonymous
hmm so the 1/2-5
anonymous
  • anonymous
if we changed the -5 to +5 then instead of 1/2-5 it would be 1/2?
phi
  • 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
  • anonymous
ok
anonymous
  • anonymous
still really weird to me
phi
  • 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
  • anonymous
ok
phi
  • phi
\[ (7^3)^{−2}\] can you rewrite this? (tread the (7^3) as one thing)
phi
  • phi
*treat
anonymous
  • anonymous
ok umm 3/7
phi
  • 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
  • anonymous
ok lets see
anonymous
  • anonymous
i believe flip the numbers around? I really dont know DD:
phi
  • phi
yes flip. think of (7^3) as one "number"
anonymous
  • anonymous
ok
anonymous
  • anonymous
so 3/7^-2?
anonymous
  • anonymous
or 3^7-2
phi
  • phi
you changed (7^3) . don't change it.
anonymous
  • anonymous
ohhh
anonymous
  • anonymous
7^3 stays the same
anonymous
  • anonymous
if we made it different it would be 7/3^2?
phi
  • phi
yes, what changes is we write 1/(7^3)^2
anonymous
  • anonymous
ohhhh
anonymous
  • anonymous
ok so the 7 stays with the 3
anonymous
  • anonymous
ok ok
phi
  • phi
we now have \[ \frac{1}{(7^3)^2}\]
anonymous
  • anonymous
ya
phi
  • phi
do you know that x^2 means x*x ?
anonymous
  • anonymous
no i didnt
phi
  • phi
do you know that 3^2 means 3*3 ?
anonymous
  • anonymous
yes
phi
  • phi
and 5^2 means 5*5
anonymous
  • anonymous
yes
phi
  • phi
what about (7^3)^2 any idea ?
anonymous
  • anonymous
hmm
anonymous
  • anonymous
I was think 7x3x2 but that wouldnt be correct right
phi
  • 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
  • anonymous
7x3 and 3x2?
phi
  • phi
would you believe (7^3)*(7^3) ?
anonymous
  • anonymous
thats how it is??
anonymous
  • anonymous
there is only 1 7^3
phi
  • 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
  • anonymous
hmmm ok
phi
  • phi
so you want to show (xyz) times itself 3 times you would write (xyz)^3
anonymous
  • anonymous
ok
anonymous
  • anonymous
so it would be 7x7x7?
anonymous
  • anonymous
if I understand correctly or 7x3?
phi
  • phi
7^3 means 7*7*7
anonymous
  • anonymous
ok i got that
phi
  • 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
  • anonymous
ohhhh
anonymous
  • anonymous
:DDD
anonymous
  • anonymous
THANK YOUU
anonymous
  • anonymous
btw I have a few more if you can help:?
phi
  • phi
if you make a new post
anonymous
  • anonymous
i will!

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