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If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 17:58
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GMATBusters’ Quant Quiz Question 1 If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)? A. 1 B. 1/2 C. 0 D. ½ E. 2
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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Updated on: 15 Feb 2020, 18:05
If \(a^m*a^n = a^{mn}\), what is the value of \(m(n2)+n(m2)\)? A. 1 B. 1/2 C. 0 D. ½ E. 2
\(a^m*a^n = a^{mn}\) => \(a^{m+n} = a^{mn}\)
=> m+n = mn
\(m(n2)+n(m2) = mn2m+nm2n = 2(mnmn) = 2(mn(m+n)) = 0\)  Answer C
Originally posted by shameekv1989 on 15 Feb 2020, 18:04.
Last edited by shameekv1989 on 15 Feb 2020, 18:05, edited 1 time in total.



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 18:04
a^m*a^n = a^mn a^m*a^n = a^m+n Hence m+n=mn m(n2)+n(m2) =2mn  2(m+n) =2mn 2mn =0
C is the answer
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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Updated on: 15 Feb 2020, 20:31
From the first formula we can find m+n=mn by simplifying the equation as did below. a^m*a^n=a^(m+n) a^(m+n)=a^mn => m+n=mm
Then we try to simplify the problem as did below m(n2)+n(m2)=mn2m+mn2m=2mn2m2n=2(mnmn)=2(mn(m+n)) As you can see the simplified outcome is 2(mn(m+n))
Since m+n=mm we can substitute m+n for mn as did below 2(mn(m+n)=2(mnmn)=O So C is right
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Originally posted by Enkhhulan on 15 Feb 2020, 18:14.
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 18:25
a^m.a^n=a^mn a^(m+n)=a^mn m+n=mn m(n2)+n(m2) =mn2m+mn2n =2mn2(m+n) =2mn2mn =0 Hence, Ans. is C.



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 18:41
The answer would be 0. This is a pretty easy one.
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 20:05
given mn = m+n equation m(n2)+n(m2) mn2m +mn2n 2mn2(m+n) from given stmt 2mn 2mn =0 thus C
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 21:35
Solution:
Question 1: If \(a^m*a^n = a^{mn}\), what is the value of \(m(n2)+n(m2)\)?
LHS = \(a^m*a^n = a^{m + n}\)
RHS = \(a^{mn} \)
By equating both the LHS and RHS, we get: \(a^{m + n} = a^{mn}\) [Equation 1]
Now, in order to find out the value of expression, \(m(n  2) + n(m  2)\), we would first expand the expression by removing the parenthesis.
Therefore, \(m(n  2) + n(m  2) = mn  2m + mn  2n = 2mn  2(m + n) = 2(mn  m  n)\) [Equation 2]
From Equation 1 we get, \(m + n = mn\) since, base is ''a'' on LHS and RHS.
Thus, \(mn  m  n = 0 \) and by substituting this value in Equation 2 we get: \(2(mn  m  n) = 2*0 = 0\), which is the answer.
Therefore, Option C i.e., 0 is the correct answer of question 1.



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 23:07
If a^m*a^n = a^mn, what is the value of m(n2)+n(m2)?
a^m*a^n = a^mn
a^(m+n) = a^mn (laws of exponent)
from here we get  (m+n) = mn now, m(n2)+n(m2) = mn2m+mn2n = 2mn2(m+n) = 2{mn(m+n)} = 0 (since m+n = mn)
C is the correct answer



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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15 Feb 2020, 23:17
a^m*a^n = a^mn a^{m+n} = a^mn m+n = mn let m=2, n=2 Substituting values of m and n in the expression m(n2)+n(m2) = 0 IMO C
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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Updated on: 16 Feb 2020, 06:21
GIVEN: \( a^{m} * a^{n} = a^{mn}\) TO FIND: m(n2)+n(m2)
given: \( a^{m} * a^{n} = a^{mn}\) => \( a^{m+n} = a^{mn}\) => \(m+n = mn \) => \(m + n  mn = 0\)  Eqn. (1)
We have to find the value of: = \( m(n2)+n(m2) \) = \( mn  2m + mn  2n \) = \( 2mn  2m  2n \) = \(2(mn  m  n)\)  Eqn. (2) = \( 2 (m + n  mn) \) {taking 1 as common from the bracket} = \( 2 ( 0 ) = 0 \) {as we know from Eqn. (1) that: m + n  mn = 0}
Hence, our answer is 0.
Originally posted by asterias on 15 Feb 2020, 23:50.
Last edited by asterias on 16 Feb 2020, 06:21, edited 1 time in total.



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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16 Feb 2020, 00:10
a^m.a^n=a^mn
a^(m+n)=a^mn
m+n=mn
Let it be equation 1
Now
m(n2)+n(m2)
=mn2m+mn2n
=2mn2(m+n)
And from equation 1 (m+n)=mn
=2mn2mn
=0



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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16 Feb 2020, 02:29
upon solving m(n2)+n(m2) we get 2(mnmn) =>2(mn  (m+n)) => 2(mnmn) => ans zero (C)



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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16 Feb 2020, 02:53
If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?A. 1 B. 1/2 C. 0 D. ½ E. 2 There should be some constraints given for a. If a = 1, then any values of m and n satisfy a^m*a^n = a^(mn). If a = 0, then any positive values of m and n satisfy a^m*a^n = a^(mn). If a = 1, also many values of m and n satisfy a^m*a^n = a^(mn). For example, m = n = even.
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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16 Feb 2020, 05:20
Solution:
a^m*a^n = a^mn => m+n=mn => mnmn = 0
for the question asked:
value of mn2m+mn2n => 2(mnmn) => 0 since mnmn = 0;
Answer : 0



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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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16 Feb 2020, 07:26
OK lets do it in within 1 minute. From the given equation :mn=m+n >2(mn(m+n))=0 So Ans: (C) 0
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Re: If a^m*a^n = a^(mn), what is the value of m(n2)+n(m2)?
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