General problem solving

Question

Been strugglinh to solve this. How did they arrive at the solution  m^{n−2}  (1 –  3m^2  +  4m^3 ).? from my manhattan gmat flashcard

the question is below

m^{n−2}  –  3m^{n}  +  4m^{n+1}

ENGRTOMBA2018 · Answer

m^{n−2}  –  3m^{n}  +  4m^{n+1}

First step should always be to take out whatever is common. In this case as  m^{n-2}  will easier to proceed with. Also, realise that  m^n = m^{n-2}*m^{2}  and  m^{n+1} = m^{n-2}*m^3

I have employed the following rule of exponents:  m^a*m^b = m^{a+b}

Once you bring every exponent in the equation to the same power (=n-2), you can now proceed to take  m^{n-2}  common from all 3 terms.

thus,  m^{n−2}  –  3m^{n}  +  4m^{n+1}  =  m^{n−2}  –  3m^{n-2}*m^2  +  4m^{n-2}*m^3

--->  m^{n−2} – 3m^{n-2}*m^2 + 4m^{n-2}*m^3  =  m^{n-2} (1-3*m^2+4m^3)  and this is your answer.

Hope this helps.

asethi · Answer

Let m=2 and n=3

Putting the values in the expression m^(n−2) – 3(m^n) + 4m^(n+1) gives the value '42'
Again putting the value in the next expression gives the same answer '42'

Hope this helps !!!

Ekland · Answer

okay.  asethi  that would be useful where there are options. that was in flashcard questions and without options. thanks though.  Engr2012  you nailed it again. you wicked mathematician. thanks a zillion times

General problem solving

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