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

- InspectorJoe

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- InspectorJoe

\[2^{6}\times2^{-3}\div2^{10}\div2^{-8}\]

- Nnesha

don't use calculator. you will not get decimal answer.

- InspectorJoe

I'm not which means I must be doing something wrong

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## More answers

- Nnesha

ohh nvm then show your work please
don't even touch the base just move around the exponents

- Nnesha

exponent rule you can't have the negative exponent \[x^{-m}=\frac{ 1 }{ x^m }\] flip the fraction to make it positive exponent

- Nnesha

\[\huge\rm \frac{ x^{-m} }{ 1 }=\frac{ 1 }{ x^m }\]

- InspectorJoe

are we talking about an imaginary base under the entire problem ? sorry

- Nnesha

imaginary base ??? :o

- Nnesha

\[\huge\rm \frac{ 2^6 \times 2^{-3} }{ \frac{ 2^{10} }{ 2^{-8}} }\] this is your question right where `2` is the base

- InspectorJoe

NO

- InspectorJoe

refer to the initial post showing the actual problem

- Nnesha

\[\huge\rm \frac{\color{reD}{ 2^6 \times 2^{-3}} }{ \frac{ 2^{10} }{ 2^{-8}} }\] solve the red part first
when you `multiply` same bases you should `add` their exponents

- InspectorJoe

okay what about the division ? my results now come back to 1^1

- Nnesha

alright \[\rm \color{Red}{2^6 \times 2^{-3} }\div 2^{10} \div 2^{-8}\]

- InspectorJoe

Yes

- Nnesha

same thing. :=)
solve the red part first

- InspectorJoe

okay than divide from left to right subtracting the exponents right?

- InspectorJoe

okay so my new answer is 4^{27}

- InspectorJoe

4^27

- Nnesha

how did you get 4 ?

- zzr0ck3r

there is nothing wrong with decimals

- InspectorJoe

2X2

- Nnesha

just play with the exponents don't even touch the base

- Nnesha

multiply the same u would add their exponents alright \[\rm \color{Red}{2^{6+(-3)} }\div 2^{10} \div 2^{-8}\] like this

- InspectorJoe

So leave the base and add and subtract the exponents? new answer\[2^{-36}\]

- InspectorJoe

correction sorry wrong numbers

- Nnesha

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

- InspectorJoe

2^21 final answer

- Nnesha

\[\huge\rm \color{black}{2^{6+(-3)} }\color{red}{\div} 2^{10} \color{red}{\div }2^{-8}\] different rule when you divide same bases \[\rm \frac{ x^m }{ x^n }=x^{m-n}\]

- InspectorJoe

okay so my results should be 2^-15

- Nnesha

how did you get -15 ?

- InspectorJoe

okay I first did 6+-3= 3
than I did 10- -8= 18
3-18=-15?

- Nnesha

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

- Nnesha

\[\huge\rm \frac{ 2^{3+(-10)} }{ 2^{-8}}\] try to solve now!

- InspectorJoe

2^1? final answer,
I did 3+-10= -7
than -7 - -8= 1
2^1

- Nnesha

YAYAY!!

- InspectorJoe

Really I though I got it wrong waohh

- InspectorJoe

but how did we went from the original problem to this?

- InspectorJoe

final one?

- Nnesha

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

- InspectorJoe

holly cow for some reason I feel lost a bit. questions can you give a practice problem to solve for you.

- Nnesha

sure sure \[\huge\rm \frac{\frac{ 3^6 \times 3^7 }{ 3^4} }{ 3^{-5} }\]

- InspectorJoe

give me a sec to resolve thanks

- zzr0ck3r

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.

- Nnesha

so why we can't leave the negative exponent when it says `simplify`

- Nnesha

:=)

- Nnesha

actually sometimes we could , depends on the answer choices :P haha

- anonymous

if you need extra help you can use this site
https://mathway.com/

- InspectorJoe

thanks pinkiepug I will

- anonymous

your welcome ^.^

- InspectorJoe

okay here is my answer and problem|dw:1440395883759:dw|

- Nnesha

uh-oh |dw:1440395977961:dw| mistake

- InspectorJoe

? humm

- Nnesha

|dw:1440396028569:dw|
move the 4 to the top when do you that sign would change
\[\frac{ x^m }{ x^{n} }=x^{m-n}\]

- InspectorJoe

it should be 13-4 = 9

- Nnesha

\(\huge\color{green}{\checkmark}\)

- InspectorJoe

than 9- (-5)= 14

- InspectorJoe

final answer 3^14

- Nnesha

perfect! great job!

- Nnesha

i'm sooooooooooooooo sleepy
gtg bye! good luck!

- InspectorJoe

thank you so much have a good night and week

- Nnesha

my pleasure /same to u!

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