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exponents problem

by LFalken » Wed Jun 10, 2009 7:32 am
What is the Value of 'm' ?

(1/5)^m * (1/4)^18 = 1/((2*(10)^35))


I believe m=35

could someone please find the time to verify this is the correct answer and explain the solution. I would be very thankful if so... I'm having trouble with this one....
LFAL
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by ssmiles08 » Wed Jun 10, 2009 7:39 am
IMO 35 as well.

1/(2*10^35) = 1/(2*(2*5)^35)

5^35 = 5^m
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by LFalken » Wed Jun 10, 2009 7:49 am
Ssmiles08,

Thank you very much! But could you elaborate some on the solution... I'm not seeing what you did with the (1/4)^18 value that (1/5)^m is multiplied by... showing a few steps would be great. Thanks!
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by LFalken » Wed Jun 10, 2009 7:50 am
Ssmiles08,

Thank you very much! But could you elaborate some on the solution... I'm not seeing what you did with the (1/4)^18 value that (1/5)^m is multiplied by... showing a few steps would be great. Thanks!
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by ssmiles08 » Wed Jun 10, 2009 8:04 am
LFalken wrote:Ssmiles08,

Thank you very much! But could you elaborate some on the solution... I'm not seeing what you did with the (1/4)^18 value that (1/5)^m is multiplied by... showing a few steps would be great. Thanks!
yes sure.

(1/5)^m * (1/4)^18 = 1/((2*(10)^35))

(1/5)^m = 1/5^m

(1/4)^18 = ((1/2)^2)^18 = 1/2^36

1/((2*(10)^35)) = 1/(2*(2*5)^35)

so its 1/5^m * 1/2^36 = 1/(2*2^35*5^35)

2*2^35 = 2^36

5^35 = 5^m
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by tohellandback » Wed Jun 10, 2009 8:06 am
LFALKEN,
(1/5)^m * (1/4)^18 = 1/((2*(10)^35))

(1/5)^m * (1/4)^18 = 1/((2*(5*2)^35))
(1/5)^m * (1/4)^18 = 1/((2*(5)^35*(2)^35))

(1/5)^m * (1/4)^18 = 1/(((5)^35*(2)^36))
(1/5)^m * (1/4)^18 = (1/5)^35 * (1/4)^18

so m=35
The powers of two are bloody impolite!!
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by LFalken » Wed Jun 10, 2009 8:23 am
ssmiles08, and tohellandback....

Thank you both very much for your responses... they both cleared things up for me. I appreciate it!
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