SOLUTION: Hi, I really need help on the following problem; I must have reworked it millions of times, but are not getting the right answer. Also, I am getting similar problems involving

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Question 426320: Hi,
I really need help on the following problem; I must have reworked it millions of times, but are not getting the right answer. Also, I am getting similar problems involving similar terms and grouping of terms wrong. Here is the problem, and here is how I did it. Thank you for you help.
[(3)^(-2) + 5*(2)^0]/[3-4(3)^(-1)]
[(3)^(-2)]/[(3-4*(3)^(-1)] + [5*(2)^0]/[3-4*(3)^0] =
1/[(3)^2] * [1(3)^1]/[3-4] + [5*1*3]/[3-4] = [3/(-9)] + 15 = -46/3
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
[(3)^(-2) + 5*(2)^0]/[3-4(3)^(-1)]
[(3)^(-2)]/[(3-4*(3)^(-1)] + [5*(2)^0]/[3-4*(3)^0] =
Except for the exponent of 0 in the second denominator, you are OK here.
1/[(3)^2] * [1(3)^1]/[3-4] + [5*1*3]/[3-4] = [3/(-9)] + 15 = -46/3
Now we run into serious problems. The -1 exponent in the denominators only apply to the 3 that is in front of it. So there is a lot wrong at this point.

%283%5E%28-2%29+%2B+5%2A%282%29%5E0%29%2F%283-4%283%29%5E%28-1%29%29
Here is how I would do it. The order of operations (aka PEMDAS) tells us to started with Parentheses. More correctly we should start with grouped expressions. Numerators and denominators count as grouped expressions, even if there are no visible parentheses. So I am going to go through the order of operations in the numerator and denominator first. Within the numerator and denominator we start with exponents:
%281%2F9+%2B+5%2A1%29%2F%283-4%281%2F3%29%29
(Remember that a none zero number to the zero power is 1 and that a%5E%28-n%29+=+1%2Fa%5En). Multiply next:
%281%2F9+%2B+5%29%2F%283-4%2F3%29
Adding and subtracting next:
%281%2F9+%2B+45%2F9%29%2F%289%2F3-4%2F3%29
%2846%2F9%29%2F%285%2F3%29
Now that we have simplified the numerator and denominator, we can simplify the fraction as a whole. Dividing a fraction by a fraction is dome by multiplying by the reciprocal of the divisor:
%2846%2F9%29%2A%283%2F5%29
As usual, we are allowed to cancel before multiplying fractions:
%2846%2F%283%2A3%29%29%2A%283%2F5%29
%2846%2F%28cross%283%29%2A3%29%29%2A%28cross%283%29%2F5%29
%2846%2F3%29%2A%281%2F5%29
Multiplying:
%2846%2F15%29
This will not reduce. But it is an improper fraction so we can convert it into a mixed number:
3%261%2F15