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If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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Updated on: 04 Oct 2017, 05:39
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If \(5^{21} * 4^{11} = 2 * 10^n\), what is the value of n? A. 11 B. 21 C. 22 D. 23 E. 32
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Originally posted by Yalephd on 08 Aug 2010, 20:12.
Last edited by Bunuel on 04 Oct 2017, 05:39, edited 4 times in total.
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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09 Aug 2010, 02:36




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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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08 Aug 2010, 20:41
My attempt: 5^(21) * 4^(11) = 2*10^p 5^(21) * 2 ^ (22) = 2 * (2*5)^p 5^(21) * 2 ^ (22) = 2 * 2^(p) * 5^(p) 5^(21) * 2 ^ (22) = 2^(p+1) * 5^(p) => (p+1) = 22 => p = 21 Answer: 21 (B)
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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09 Aug 2010, 03:57
I got it now using ezhilkumarank's method. Thanks. Bunuel, I don't follow your method. Are you saying that 5^21 * 4^11 = 2 * 2^21 * 5^21



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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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09 Aug 2010, 05:15
Yalephd,
What Bunuel is trying to say is that save time by considering only 5
We have 10^p = (2*5)^p = 2^p * 5^p



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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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14 Aug 2010, 15:12
vasili wrote: Can somebody please put detailed explanation? Thanks.
If 5^21 x 4^11=2x10^n, what's n?
11 21 22 23 32 @ vasili  This question is already answered in one of the earlier post. Kindly search for the question once before posting. 5^21 * 4^11=2*10^n = 5^21 * 4^11=2*(2*5)^n = 5^21 * 4^11 = 2^(n+1) * 5^n => n = 21.
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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23 Aug 2010, 08:36
5^21 2^22 = 2 10^n 10^21 = 10^n Hence n = 21 Posted from my mobile device
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Re: If 5^21*4^11 = 2*10^n, what is the value of n?
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05 Feb 2011, 21:40
These types are usually solved by reducing the term to prime factors and few common rules of exponent. 5^21 * 4^11 = 2 * 10^n Consider the bases first; 5,4,2,10 5 and 2 are already primes; 4 and 10 composites. Reduce these to prime factors: 4=2*2 10=5*2 Place in the equation: \(5^{21} * 4^{11} = 2 * 10^n\) \(5^{21} * (2*2)^{11} = 2 * (2*5)^n\) \(5^{21} * (2)^{11} *(2)^{11}= 2 * (2)^n*(5)^n\) ##\((x*y)^m = x^m * y^m\)#### Rule of exponent## \(5^{21} * (2)^{22} = (5)^n * 2^{(n+1)}\) ##\(x^m*x^n = x^{(m+n)}\)## Rule of exponent## Compare LHS and RHS n+1=22 n=21 Ans: "B"
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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Updated on: 04 Aug 2013, 10:36
njkhokh wrote: If 5^21 x 4^11 = 2 x 10^n what is the value of n?
A) 11 B) 21 C) 22 D) 23 E) 32 \(5^21\)\(*4^11\) \(= 2*10^n\) \(5^21* 2^22 = 2 *10^n\) ( AS \(4^11= (2^2)^11\)) \((5.2)^21 * 2 = 2 * 10^n\) HENCE n = 21
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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04 Aug 2013, 10:36
njkhokh wrote: If 5^21 x 4^11 = 2 x 10^n what is the value of n? A) 11 B) 21 C) 22 D) 23 E) 32 5^21 x 4^11 = 2 x 10^n 5^21 x 2^22 = 2 x 10^n 2 x 5^21 x 2^21 = 2 x 10^n 2 x 10^21 = 2 x 10^n Thus n = 21 Answer B
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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Updated on: 15 Apr 2014, 00:56
\(5^{21} * 4^{11} = 2*10^p\) \(5^{21} * 2^{22} = 2*10^p\) \(2 * 2^{21} * 5^{21} = 2*10^p\) \(2 * 10^{21} = 2*10^p\) Equating powers, p = 21 = Answer B
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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14 Apr 2014, 17:23
ausadj18 wrote: hi, all!
quick exponent question which seems easy but i cant seem to get my head around it  reallly appreciate your help!!
If 5^21 x 4^11 = 2 x 10^n,, what is value of n?
answer is 21, but honestly cant remember quite how to get here  thanks again for any help! Thumb rule for any exponents question: Deal only in prime numbers. \(5^{21} * 4^{11} = 2 * 10^n\) \(5^{21} * 2^{22} = 2 * 2^n * 5^n\) \(5^{21} * 2^{22} = 2^{n+1} * 5^n\) Now match the exponents of same prime numbers. Power of 5 on both sides should be equal. 21 = n or Power of 2 on both sides should be equal. 22 = n+1 n = 21
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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27 Aug 2016, 22:53
SharmaShruti wrote: 5^21 X 4^11 = 2 X 10^n. What is the value of n? a) 11 b) 21 c) 22 d) 23 e)32 The given expression \(5^21 * 4^(11) = 2 * 10^n\) can be written as \(5^21 * 2^22 = 2 * 5^n * 2^n\) or \(5^21 * 2^22 = 5^n * 2^(n+1)\) Comparing the powers of 2 on both sides, we will have \(2^22 = * 2^(n+1)\) or 22=n+1 or n=21. hence B
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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28 Aug 2016, 05:38
SharmaShruti wrote: 5^21 X 4^11 = 2 X 10^n. What is the value of n? a) 11 b) 21 c) 22 d) 23 e)32 Hi, One does not require to simplify anything.. On left hand side, the power of 5 is 21..... But on right side it is part of 10.. so power of 10 has to be same as that of 5.. Ans 21
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Re: If 5^21 * 4^11 = 2 * 10^n, what is the value of n?
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06 Oct 2017, 09:53
Yalephd wrote: If \(5^{21} * 4^{11} = 2 * 10^n\), what is the value of n?
A. 11 B. 21 C. 22 D. 23 E. 32 We can simplify the given equation: 5^21 x 2^22 = 2^1 x 10^n 5^21 x 2^21 = 10^n 10^21 = 10^n 21 = n Answer: B
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Re: If 5^21 x 4^11= 2 x 10^n what is the value of n? a. 11 b. 21
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