SOLUTION: Will you please help me solve (1/3) to the m power is equal to 27 to the m+2 power?

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Question 189523This question is from textbook Algebra 2
: Will you please help me solve (1/3) to the m power is equal to 27 to the m+2 power? This question is from textbook Algebra 2

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F3%29%5Em=%2827%29%5E%28m%2B2%29 Start with the given equation.


%283%5E%28-1%29%29%5Em=%2827%29%5E%28m%2B2%29 Rewrite 1%2F3 as 3%5E%28-1%29


%283%5E%28-1%29%29%5Em=%283%5E3%29%5E%28m%2B2%29 Rewrite 27 as 3%5E3


3%5E%28-m%29=3%5E%283%28m%2B2%29%29 Multiply the exponents.


-m=3%28m%2B2%29 Since the bases are equal, the exponents are equal.


-m=3m%2B6 Distribute.


-m-3m=6 Subtract 3m from both sides.


-4m=6 Combine like terms on the left side.


m=%286%29%2F%28-4%29 Divide both sides by -4 to isolate m.


m=-3%2F2 Reduce.


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Answer:

So the answer is m=-3%2F2 which in decimal form is m=-1.5.