SOLUTION: If {{{a^m*a^n=a^mn}}},then m(n-2)+n(m-2)is?options are (a)-1,(b)1 (c)0 (d)1/2

Question 458405: If ,then m(n-2)+n(m-2)is?options are (a)-1,(b)1 (c)0 (d)1/2
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Use the idea that to state that is also the same as

Now, if the bases are equal, then the exponents are equal. So or

Now all we need to do is start with m(n-2)+n(m-2) and simplify

m(n-2)+n(m-2)

mn-2m+nm-2n

mn-2m+mn-2n

mn+mn-2m-2n

2mn-2(m+n)

2(m+n)-2(m+n) .... Note: I've replaced mn with m+n (since )

0

So all this shows us that m(n-2)+n(m-2) = 0 when m+n = mn

Consequently, this means that m(n-2)+n(m-2) = 0 if

So the answer is choice C)
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