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Can't figure out the exponent problem

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Intern
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Can't figure out the exponent problem  [#permalink]

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New post 25 Aug 2011, 09:15
1
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A
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Difficulty:

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Question Stats:

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Can someone please help me figure this out? Can you combine exponents when both the base and exponent are different?
5^21 * 4^11 = 2*10^n
What is the value of n?
A) 11
B)21
C)22
D)23
E)32

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Re: Can't figure out the exponent problem  [#permalink]

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New post 25 Aug 2011, 09:29
21.

5^21*2^2*11=5^21*2^22= 2*5^21*2^21 =2*10^21
2*10^21=2*10^n
n=21
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Re: Can't figure out the exponent problem  [#permalink]

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New post 25 Aug 2011, 10:01
Ok, I follow you up until 2*5^21*2^21 =2*10^21. I don't see where you get the é that you're multiplying the five by. Did you just tak it out of 2^22?
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Re: Can't figure out the exponent problem  [#permalink]

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New post 25 Aug 2011, 13:15
5^21 * 4^11 = 2^10 * 10^n

bring all the terms to comparable bases: When you keep the exponent the same you can break the number down so 4^11 = 2^11 * 2^11 or (much easier for this problem) you can say 4 = 2^2 so (2^2)^11 which is 2^22, since you multiply the exponents .10^n = 5^n * 2^n,

so we get:

5^21 * 2^22 = 2^1 * 5^n * 2^n

when you compare the equation, 5^21 = 5^n and 2^22 = 2^1 * 2^n

As the bases are the same then you can direct compare the exponents (Its like saying one apple + one pear = one pear + one apple, they are directly equal).

Also, with multiplying exponential terms with the same base, you add the exponents. ( I just envision the x standing upright to make a +). So they form the equations 21 = n (nice and easy) and 22 = 1 + n which also works out to n = 21

( I would have used the {m} setting but it was't handling the 21 and 11 very well)
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Re: Can't figure out the exponent problem  [#permalink]

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New post 25 Aug 2011, 15:11
5^21 * 4^11 = 2* 10^n

5^21 * (2^2)^11 = 2 * (2*5)^n

5^21 * 2^22 = 2^(n+1) * 5^n

equating powers of 5 , we can see n = 21.

Answer is B.
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Re: Can't figure out the exponent problem  [#permalink]

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New post 26 Aug 2011, 01:53
Thank you all soooo much for your help! I finally understand what I did wrong!
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Re: Can't figure out the exponent problem  [#permalink]

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Re: Can't figure out the exponent problem &nbs [#permalink] 22 Jan 2016, 08:27
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