SOLUTION: Simplify and write the result without negative exponents. ((-3a^(-2) b^(-3) c^0 )^(-2))/((-2a^4 b^2 c^(-2) )^3 )

Algebra ->  Exponents-negative-and-fractional -> SOLUTION: Simplify and write the result without negative exponents. ((-3a^(-2) b^(-3) c^0 )^(-2))/((-2a^4 b^2 c^(-2) )^3 )       Log On


   

Question 250629: Simplify and write the result without negative exponents.
((-3a^(-2) b^(-3) c^0 )^(-2))/((-2a^4 b^2 c^(-2) )^3 )
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
your equation the way you wrote it looks like this:



That doesn't look right.

I think you may have wanted it to look like this:



I will assume my interpretation is correct and will solve for that.

Sinplify numerator and denominator by removing the outermost parentheses.

since %28x%5Ea%2Ay%5Eb%29%5Ec+=+x%5E%28a%2Ac%29%2Ay%5E%28b%2Ac%29, your equation becomes:



a%5E4%2Fa%5E12 = a%5E%284-12%29 = a%5E%28-8%29 = 1%2Fa%5E8

b%5E6%2Fb%5E6 = 1%2F1

c%5E0%2Fc%5E%28-6%29 = c%5E0-%28-6%29 = c%5E6

your equation becomes:

%28-3%5E%28-2%29%2Ac%5E6%29%2F%28-2%5E%283%29%2Aa%5E%288%29%29

-3%5E%28-2%29 = 1%2F%28-3%5E2%29 = %281%2F9%29

-2%5E3 = -8

your equation becomes:

%28%281%2F9%29%2Ac%5E6%29%2F%28%28-8%29%2Aa%5E%288%29%29

multiply numerator and denominator of this equation by 9 and you get:


c%5E6%2F%28%28-72%29%2Aa%5E%288%29%29

to confirm this answer is correct, we need to substitute some values in both the original equation and the final equation to see that they come out with the same answer.

we'll use:

a = 3
b = 4
c = 5

the original equation is:



after substitution, this becomes:



perorming indicated operations, this becomes:



simplifying, this becomes:

36864/-1114512556 = -.033076343

the final equation is:

c%5E6%2F%28%28-72%29%2Aa%5E%288%29%29

after substitution, this becomes:

%285%29%5E6%2F%28%28-72%29%2A%283%29%5E%288%29%29

this becomes:

15625 / -472392 = -.033076343

since the answer from the original equation and the final equation are the same, the simplification looks good.

your original equation of
simplifies to c%5E6%2F%28%28-72%29%2Aa%5E%288%29%29