SOLUTION: Perform the indicated operations (-1/5)power of 3 {(-1/3)power of 2 + 1/12(1/6 - (-1/4)power of 3)}

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Question 72989: Perform the indicated operations
(-1/5)power of 3 {(-1/3)power of 2 + 1/12(1/6 - (-1/4)power of 3)}
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
%28-1%2F5%29%5E3%28%28-1%2F3%29%5E2+%2B+%281%2F12%29%2A%281%2F6+-+%28-1%2F4%29%5E3%29%29Start with given expression
%28%28-1%29%5E3%2F5%5E3%29%28%28%28-1%29%5E2%2F3%5E2%29+%2B+%281%2F12%29%2A%281%2F6+-+%28%28-1%29%5E3%2F4%5E3%29%29%29Distribute the exponents to both numerators and denominators with exponents
Any negative number raised to a odd power will have a negative sign (ie %28-1%29%5E3=-1) and any negative number raised to a even power will have a positive sign ie (%28-1%29%5E4=1).
%28%28-1%29%2F125%29%28%281%2F9%29+%2B+%281%2F12%29%2A%281%2F6+-+%28%28-1%29%2F64%29%29%29Simplify the exponents
%28%28-1%29%2F125%29%281%2F9+%2B+1%2F72+%2B+1%2F768%29%29Distribute the 1/12
%28%28-1%29%2F125%29%28%28256%2B32%2B3%29%2F2304%29%29 Add the values in the parenthesis (I found the LCD of 2304 and added the corresponding numerators)
%28%28-1%29%2F125%29%28%28291%29%2F2304%29%29Multiply the fractions
%28%28-291%29%2F288000%29%29Simplify
-97%2F96000=-0.00101041666Approximately note: the last group of 6's repeat forever.
Hope that helps. I know there are a lot of steps that I glossed over (I'm assuming you have adequate knowledge of order of operations, exponents, fractions, etc.), so ask about any step I explained.