SOLUTION: (c^-1)^-12(c^-5)^6/(c^-4)^0(c^3)^-3 answer 1/c^9 How do I get there? I am so lost! please help

Algebra ->  Algebra  -> Exponents-negative-and-fractional -> SOLUTION: (c^-1)^-12(c^-5)^6/(c^-4)^0(c^3)^-3 answer 1/c^9 How do I get there? I am so lost! please help       Log On

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Question 150455: (c^-1)^-12(c^-5)^6/(c^-4)^0(c^3)^-3
answer 1/c^9
How do I get there? I am so lost! please help

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Let's break this problem down.


First let's simplify the numerator


%28c%5E%28-1%29%29%5E%28-12%29 Start with the first term in the numerator


c%5E%28%28-1%29%28-12%29%29 Multiply the exponents using the identity %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29


c%5E%2812%29 Multiply -1 and -12 to get 12


So %28c%5E%28-1%29%29%5E%28-12%29 simplifies to c%5E%2812%29


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%28c%5E%28-5%29%29%5E%286%29 Move onto the second term in the numerator


c%5E%28%28-5%29%286%29%29 Multiply the exponents using the identity %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29


c%5E%28-30%29 Multiply -5 and 6 to get -30


So %28c%5E%28-5%29%29%5E%286%29 simplifies to c%5E%28-30%29



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So the expression %28%28c%5E%28-1%29%29%5E%28-12%29%28c%5E%28-5%29%29%5E%286%29%29%2F%28%28c%5E-4%29%5E%280%29%28c%5E3%29%5E%28-3%29%29 now becomes %28c%5E%2812%29c%5E%28-30%29%29%2F%28%28c%5E-4%29%5E%280%29%28c%5E3%29%5E%28-3%29%29



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Now let's simplify the denominator


%28c%5E%28-4%29%29%5E%280%29 Start with the first term in the denominator


c%5E%28%28-4%29%280%29%29 Multiply the exponents using the identity %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29


c%5E%280%29 Multiply -4 and 0 to get 0


1 Raise c to the zeroth power to get 1


So %28c%5E%28-4%29%29%5E%280%29 simplifies to 1


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%28c%5E%283%29%29%5E%28-3%29 Move onto the second term in the denominator


c%5E%28%283%29%28-3%29%29 Multiply the exponents using the identity %28x%5E%28y%29%29%5Ez=x%5E%28y%2Az%29


c%5E%28-9%29 Multiply 3 and -3 to get -9


So %28c%5E%283%29%29%5E%28-3%29 simplifies to c%5E%28-9%29



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So after simplification, we go from %28c%5E%2812%29c%5E%28-30%29%29%2F%28%28c%5E-4%29%5E%280%29%28c%5E3%29%5E%28-3%29%29 to %28c%5E%2812%29c%5E%28-30%29%29%2F%28%281%29c%5E%28-9%29%29



%28c%5E%2812%29c%5E%28-30%29%29%2F%28%281%29c%5E%28-9%29%29 Start with the given expression.


%28c%5E%2812%29c%5E%28-30%29%29%2F%28c%5E%28-9%29%29 Multiply 1 and c%5E%28-9%29 to get c%5E%28-9%29


%28c%5E%2812%2B%28-30%29%29%29%2F%28c%5E%28-9%29%29 Multiply the terms in the numerator by adding the exponents.


%28c%5E%28-18%29%29%2F%28c%5E%28-9%29%29 Add 12 to -30 to get -18


c%5E%28-18-%28-9%29%29 Divide the terms by subtracting the exponents.


c%5E%28-18%2B9%29 Rewrite -18-%28-9%29 to get -18%2B9


c%5E%28-9%29 Add -18 to 9 to get -9


1%2F%28c%5E%289%29%29 Rewrite c%5E%28-9%29 as 1%2F%28c%5E%289%29%29 to make the exponent positive.



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Answer:

So %28%28c%5E%28-1%29%29%5E%28-12%29%28c%5E%28-5%29%29%5E%286%29%29%2F%28%28c%5E-4%29%5E%280%29%28c%5E3%29%5E%28-3%29%29 simplifies to 1%2F%28c%5E%289%29%29