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Exponent Basic Problem - need help

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Exponent Basic Problem - need help [#permalink] New post 27 May 2009, 15:51
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5^21 x 4^11 = 2 x 10^n
n=?
:x
please show work, i'm lost. thanks in advance..
Manager
Manager
Affiliations: Beta Gamma Sigma
Joined: 14 Aug 2008
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Schools: Harvard, Penn, Maryland
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Re: Exponent Basic Problem - need help [#permalink] New post 27 May 2009, 17:24
Original equation

5^21 * 4^11 = 2*10^n

First, factor out the equation ( 5 ( 5 ) = 5*5*5*5*5 ) or 5 fives

5(21) * 4(11) = 2 * 10(N)

Next, divide both sides by 2

5(21) * 4(10) * 2 = 10(N)

simplify 4(10) to 2(20)

5(21) * 2(21) = 10(N)

5*2=10, so 21 fives times 21 twos equals 21 tens

10(21) = 10(N)

and then you have the answer

n=21

I always find it easier to work with the numbers if its factored, you can do it keeping it in exponents, because a^x / a^y = a^(x-y) and what have you, but I usually just factor them.
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Re: Exponent Basic Problem - need help [#permalink] New post 27 May 2009, 17:42
Quote:
5^21 x 4^11 = 2 x 10^n
n=?

please show work, i'm lost. thanks in advance..


5^21 * 4^11=2*10^n
==>5^21 *2^11*2^11= 5^21*2^22=10^21 * 2
==>10^21*2 =2*10^n
therefore n=21
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Re: Exponent Basic Problem - need help [#permalink] New post 27 May 2009, 23:25
thx guys, that helped a lot! :lol:
Re: Exponent Basic Problem - need help   [#permalink] 27 May 2009, 23:25
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