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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:

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

Please help me..thank you very much!

juriemagic Feb 6, 2019

#1**+2 **

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**

itsyaboi Feb 6, 2019

#3**+1 **

Thanks itsyaboi,

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

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

.Melody Feb 6, 2019

#4**+2 **

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

#6**+1 **

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

#7**0 **

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