Im trying to solve this problem and my answer keep coming up in decimals. need help 2^6X2^-3/20^10/2-8

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Im trying to solve this problem and my answer keep coming up in decimals. need help 2^6X2^-3/20^10/2-8

Mathematics
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\[2^{6}\times2^{-3}\div2^{10}\div2^{-8}\]
don't use calculator. you will not get decimal answer.
I'm not which means I must be doing something wrong

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ohh nvm then show your work please don't even touch the base just move around the exponents
exponent rule you can't have the negative exponent \[x^{-m}=\frac{ 1 }{ x^m }\] flip the fraction to make it positive exponent
\[\huge\rm \frac{ x^{-m} }{ 1 }=\frac{ 1 }{ x^m }\]
are we talking about an imaginary base under the entire problem ? sorry
imaginary base ??? :o
\[\huge\rm \frac{ 2^6 \times 2^{-3} }{ \frac{ 2^{10} }{ 2^{-8}} }\] this is your question right where `2` is the base
NO
refer to the initial post showing the actual problem
\[\huge\rm \frac{\color{reD}{ 2^6 \times 2^{-3}} }{ \frac{ 2^{10} }{ 2^{-8}} }\] solve the red part first when you `multiply` same bases you should `add` their exponents
okay what about the division ? my results now come back to 1^1
alright \[\rm \color{Red}{2^6 \times 2^{-3} }\div 2^{10} \div 2^{-8}\]
Yes
same thing. :=) solve the red part first
okay than divide from left to right subtracting the exponents right?
okay so my new answer is 4^{27}
4^27
how did you get 4 ?
there is nothing wrong with decimals
2X2
just play with the exponents don't even touch the base
multiply the same u would add their exponents alright \[\rm \color{Red}{2^{6+(-3)} }\div 2^{10} \div 2^{-8}\] like this
So leave the base and add and subtract the exponents? new answer\[2^{-36}\]
correction sorry wrong numbers
no.. i said when you `multiply` the same bases then u should add \[\huge\rm \color{Red}{2^6 \color{blue}{\times }2^{-3} }\div 2^{10} \div 2^{-8}\] here are multiplying 2^6 times 2^{-3 that's why we should add the base
2^21 final answer
\[\huge\rm \color{black}{2^{6+(-3)} }\color{red}{\div} 2^{10} \color{red}{\div }2^{-8}\] different rule when you divide same bases \[\rm \frac{ x^m }{ x^n }=x^{m-n}\]
okay so my results should be 2^-15
how did you get -15 ?
okay I first did 6+-3= 3 than I did 10- -8= 18 3-18=-15?
thanks for showing your work much appreciated ! \[\huge\rm \frac{ \color{ReD}{\frac{ 2^3 }{ 2^{10}}} }{ 2^{-8} }\] first solve the red part we should move the 10 to the top first and then
\[\huge\rm \frac{ 2^{3+(-10)} }{ 2^{-8}}\] try to solve now!
2^1? final answer, I did 3+-10= -7 than -7 - -8= 1 2^1
YAYAY!!
Really I though I got it wrong waohh
but how did we went from the original problem to this?
final one?
we used two exponents rule! \[\huge\rm \frac{ x^m }{ x^n }=x^{m-n}\] divide same base \[\huge\rm x^m \times x^n = x^{m \times n}\] when you multiply same bsses
holly cow for some reason I feel lost a bit. questions can you give a practice problem to solve for you.
sure sure \[\huge\rm \frac{\frac{ 3^6 \times 3^7 }{ 3^4} }{ 3^{-5} }\]
give me a sec to resolve thanks
I want to make one thing clear: you are of course allowed to have negative exponents it is just that your teacher wants to make sure you can go back and fourth.
so why we can't leave the negative exponent when it says `simplify`
:=)
actually sometimes we could , depends on the answer choices :P haha
if you need extra help you can use this site https://mathway.com/
thanks pinkiepug I will
your welcome ^.^
okay here is my answer and problem|dw:1440395883759:dw|
uh-oh |dw:1440395977961:dw| mistake
? humm
|dw:1440396028569:dw| move the 4 to the top when do you that sign would change \[\frac{ x^m }{ x^{n} }=x^{m-n}\]
it should be 13-4 = 9
\(\huge\color{green}{\checkmark}\)
than 9- (-5)= 14
final answer 3^14
perfect! great job!
i'm sooooooooooooooo sleepy gtg bye! good luck!
thank you so much have a good night and week
my pleasure /same to u!

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