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# Just algebra

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Hi clever people!!,..please this morning i have 3 sums for you guys..i am totally stumped by these!

it says to simplify without a calculator:

$${5^{m-2}*2^{m+2}} \over 10^m-10^{m-1}*2$$

Feb 6, 2019

#1
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Factoring the bottom yields (1-1/5) times 10^m

Now, you have the fraction: (5^(m-2 * 2^(m+2)))/((4/5)*10^m)

10^m can be expressed as 2^m * 5^m

Cancelling yields:

4/(5^2 times 4/5)

4/20 = 1/5

Feb 6, 2019
#2
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wow!,

thank you sooo much!..really appreciated!!

juriemagic  Feb 6, 2019
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Nice, itsyaboi...!!!!

CPhill  Feb 6, 2019
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Thanks itsyaboi,

I'd just like to have a go at it too :)

$${5^{m-2}*2^{m+2}} \over 10^m-10^{m-1}*2\\~\\ =[{5^{m-2}*2^{m+2}} ]\div [10^m-10^{m-1}*2]\\~\\ =[{5^{m-2}*2^{m-2}*2^4} ]\div [10*10^{m-1}-10^{m-1}*2]\\~\\ =[10^{m-2}*2^4 ]\div [10^{m-1}(10-2)]\\~\\ =[10^{m-2}*16 ]\div [10^{m-1}(8)]\\~\\ =10^{m-2-(m-1)}*2 \\~\\ =10^{-1}*2 \\~\\ =\frac{2}{10}\\~\\ =\frac{1}{5}$$

.
Feb 6, 2019
#4
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Melody!!!!!..always to the rescue..lol....thank you!!

You know..this must be telepathy of some sort because I also came across a different approach for this sum in which there was this piece:

$$(10-2)*10^{m-1}$$

and I was about to ask here for an explanation as to how this step is achieved, and walla!!..you have it in your response!!..thank you again Melody!

juriemagic  Feb 6, 2019
edited by juriemagic  Feb 6, 2019
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Melody  Feb 6, 2019
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thank you Melody,

please forgive my stupidness...I have now studied your second step....I don't understand how we can just multiply the bottom part by 10. which math law is at work here?...from step 3 onwards I fully understand, it really is just step 2...would you mind teaching me please?

juriemagic  Feb 6, 2019
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Juriemagic, you are definitely not stupid and it is not a word you should use, especially not on yourself :)

All I have said is

$$10^m\\=10^{m-1+1}\\=10^{m-1}\cdot10^1\\=10^{m-1}\cdot10\\=10\cdot 10^{m-1}$$

If you still can't work it out then say so :)

Melody  Feb 6, 2019
edited by Melody  Feb 6, 2019
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Melody is right! You should not use that word on yourself.

You should let us use it on you, because we are professionals and we know how to use it correctly.

Guest Feb 6, 2019
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Thank you Melody!,,2 lessons learnt!!...stay blessed!

juriemagic  Feb 6, 2019
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LOL

Melody  Feb 6, 2019
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Thanks, Melody.....this is a clever little problem....

CPhill  Feb 6, 2019